577:
230:
1210:
1281:
881:
976:
430:
749:
415:
1414:
1814:
1372:
97:
1700:
Dzhaparidze, K. O.; Nikulin, M. S. (1982). "Probability distributions of the
Kolmogorov and omega-square statistics for continuous distributions with shift and scale parameters".
806:
2349:
1305:
1004:
909:
774:
1030:
2173:
620:
685:
2776:
1769:
2306:
2286:
2690:
2607:
2617:
2291:
121:
2301:
2659:
2374:
2556:
2846:
2836:
2359:
1690:
1668:
1634:
2746:
2710:
2663:
1101:
3014:
2751:
1218:
1861:
1762:
819:
3045:
2816:
2394:
2364:
920:
2667:
2651:
2861:
2566:
1786:
572:{\displaystyle f\mapsto G_{n}f={\sqrt {n}}(P_{n}-P)f={\sqrt {n}}\left({\frac {1}{n}}\sum _{i=1}^{n}f(X_{i})-\mathbb {E} f\right)}
105:
2766:
2731:
2700:
2695:
2334:
2131:
2048:
1065:
1045:
47:
2705:
2033:
2329:
2136:
1544:
2055:
1451:
690:
319:
2791:
2671:
3019:
2796:
2632:
2531:
2516:
1928:
1844:
1755:
2806:
2442:
334:
2801:
1446:
1375:
2404:
1053:
1988:
1933:
1849:
2736:
2726:
2369:
2339:
1471:
Mojirsheibani, M. (2007). "Nonparametric curve estimation with missing data: A general empirical process approach".
3040:
2741:
1906:
1804:
1381:
2452:
2028:
1809:
2821:
2622:
2536:
2521:
1911:
622:
63:
2655:
2541:
1963:
1313:
2043:
2018:
1441:
2761:
2344:
1879:
2956:
2946:
2637:
2419:
2158:
2023:
1834:
2241:
2898:
2826:
2085:
2921:
2903:
2883:
2878:
2597:
2429:
2409:
2256:
2199:
2038:
1948:
583:
298:
55:
2389:
779:
2996:
2951:
2941:
2682:
2627:
2602:
2571:
2551:
2311:
2296:
2163:
1612:. Cambridge Studies in Advanced Mathematics. Vol. 63. Cambridge, UK: Cambridge University Press.
1037:
282:
1286:
985:
890:
2991:
2831:
2756:
2561:
2321:
2231:
2121:
754:
626:
302:
1013:
2961:
2926:
2841:
2811:
2581:
2576:
2399:
2236:
1901:
1839:
1778:
1717:
242:
43:
35:
2642:
1044:: sets of functions with the useful property that empirical processes indexed by these classes
2981:
2786:
2437:
2194:
2111:
2080:
1973:
1943:
1799:
1794:
1686:
1678:
1664:
1630:
1556:"Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems"
1540:
589:
59:
51:
2647:
2384:
3001:
2888:
2771:
2141:
2116:
2065:
1993:
1916:
1869:
1709:
1656:
1622:
1594:
1567:
1511:
1480:
1049:
660:
54:, limit theorems (as the number of objects becomes large) are considered and generalise the
2966:
2866:
2851:
2612:
2546:
2224:
2168:
2151:
1896:
1417:
1041:
28:
2781:
2013:
17:
2971:
2936:
2856:
2462:
2209:
2126:
2095:
2090:
2070:
2060:
2003:
1998:
1978:
1958:
1923:
1891:
1874:
326:
3034:
2873:
2414:
2251:
2246:
2204:
2146:
1968:
1884:
1824:
1721:
1644:
278:
2931:
2893:
2447:
2379:
2268:
2263:
2075:
2008:
1983:
1819:
2511:
2976:
2495:
2490:
2485:
2475:
2278:
2219:
2214:
2178:
1938:
1829:
1648:
1741:
1735:
1484:
2986:
2526:
2470:
2354:
1626:
1572:
1555:
1516:
1499:
225:{\displaystyle F_{n}(x)={\frac {1}{n}}\sum _{i=1}^{n}I_{(-\infty ,x]}(X_{i}),}
1599:
1582:
2480:
1660:
1683:
Weak
Convergence and Empirical Processes: With Applications to Statistics
2307:
Generalized autoregressive conditional heteroskedasticity (GARCH) model
1747:
1713:
1205:{\displaystyle F_{n}(x)=P_{n}((-\infty ,x])=P_{n}I_{(-\infty ,x]}.}
1276:{\displaystyle {\mathcal {C}}=\{(-\infty ,x]:x\in \mathbb {R} \}.}
1742:
Introduction to
Empirical Processes and Semiparametric Inference
1619:
Introduction to
Empirical Processes and Semiparametric Inference
876:{\displaystyle {\bigl (}G_{n}(c){\bigr )}_{c\in {\mathcal {C}}}}
1751:
1069:
971:{\displaystyle {\bigl (}G_{n}f{\bigr )}_{f\in {\mathcal {F}}}}
325:
A centered and scaled version of the empirical measure is the
62:. Applications of the theory of empirical processes arise in
1292:
1224:
991:
961:
896:
866:
301:. Glivenko and Cantelli strengthened this result by proving
1036:
A significant result in the area of empirical processes is
2287:
Autoregressive conditional heteroskedasticity (ARCH) model
1215:
In this case, empirical processes are indexed by a class
1815:
Independent and identically distributed random variables
1744:, by Michael Kosorok, another textbook available online.
98:
independent and identically-distributed random variables
2292:
Autoregressive integrated moving average (ARIMA) model
744:{\displaystyle N(0,\mathbb {E} (f-\mathbb {E} f)^{2})}
687:
converges in distribution to a normal random variable
269:) is a sequence of random variables which converge to
1384:
1316:
1289:
1221:
1104:
1016:
988:
923:
893:
822:
782:
757:
693:
663:
592:
433:
337:
124:
115:), the empirical distribution function is defined by
1500:"Generalization of the Theorem of Glivenko-Cantelli"
2914:
2719:
2681:
2590:
2504:
2461:
2428:
2320:
2277:
2187:
2104:
1860:
1785:
1653:
Empirical
Processes with Applications to Statistics
410:{\displaystyle G_{n}(A)={\sqrt {n}}(P_{n}(A)-P(A))}
1408:
1366:
1299:
1275:
1204:
1024:
998:
970:
903:
875:
800:
768:
743:
679:
614:
571:
409:
224:
1539:(Third ed.). New York: John Wiley and Sons.
1052:. While it can be shown that Donsker classes are
2174:Stochastic chains with memory of variable length
1738:, by David Pollard, a textbook available online.
1583:"Central Limit Theorems for Empirical Measures"
1763:
1473:Journal of Statistical Planning and Inference
1409:{\displaystyle \ell ^{\infty }(\mathbb {R} )}
947:
926:
852:
825:
8:
1736:Empirical Processes: Theory and Applications
1267:
1232:
1006:, a collection of measurable functions from
2302:Autoregressiveâmoving-average (ARMA) model
1770:
1756:
1748:
1367:{\displaystyle {\sqrt {n}}(F_{n}(x)-F(x))}
1598:
1571:
1515:
1399:
1398:
1389:
1383:
1331:
1317:
1315:
1291:
1290:
1288:
1263:
1262:
1223:
1222:
1220:
1178:
1168:
1131:
1109:
1103:
1018:
1017:
1015:
990:
989:
987:
960:
959:
952:
946:
945:
935:
925:
924:
922:
895:
894:
892:
865:
864:
857:
851:
850:
834:
824:
823:
821:
792:
784:
783:
781:
759:
758:
756:
732:
721:
720:
707:
706:
692:
668:
662:
597:
591:
557:
556:
544:
528:
517:
503:
491:
470:
456:
444:
432:
420:It induces a map on measurable functions
374:
360:
342:
336:
210:
182:
172:
161:
147:
129:
123:
911:, a collection of measurable subsets of
46:that characterizes the deviation of the
1463:
1056:, the converse is not true in general.
2608:Doob's martingale convergence theorems
2360:Constant elasticity of variance (CEV)
2350:ChanâKarolyiâLongstaffâSanders (CKLS)
1560:The Annals of Mathematical Statistics
1504:The Annals of Mathematical Statistics
7:
29:Process control § Control model
1307:is a Donsker class, in particular,
27:For the process control topic, see
2847:Skorokhod's representation theorem
2628:Law of large numbers (weak/strong)
1390:
1241:
1185:
1146:
653:. Similarly, for a fixed function
189:
25:
2817:Martingale representation theorem
1621:. Springer Series in Statistics.
801:{\displaystyle \mathbb {E} f^{2}}
2862:Stochastic differential equation
2752:Doob's optional stopping theorem
2747:DoobâMeyer decomposition theorem
1066:empirical distribution functions
106:cumulative distribution function
2732:Convergence of random variables
2618:FisherâTippettâGnedenko theorem
48:empirical distribution function
2330:Binomial options pricing model
1610:Uniform Central Limit Theorems
1403:
1395:
1361:
1358:
1352:
1343:
1337:
1324:
1300:{\displaystyle {\mathcal {C}}}
1250:
1235:
1194:
1179:
1158:
1155:
1140:
1137:
1121:
1115:
999:{\displaystyle {\mathcal {F}}}
904:{\displaystyle {\mathcal {C}}}
846:
840:
738:
729:
711:
697:
609:
603:
550:
537:
482:
463:
437:
404:
401:
395:
386:
380:
367:
354:
348:
216:
203:
198:
183:
141:
135:
1:
2797:Kolmogorov continuity theorem
2633:Law of the iterated logarithm
1702:Journal of Soviet Mathematics
769:{\displaystyle \mathbb {E} f}
649:))) for fixed measurable set
2802:Kolmogorov extension theorem
2481:Generalized queueing network
1989:Interacting particle systems
1447:Weak convergence of measures
1025:{\displaystyle \mathbb {R} }
1934:Continuous-time random walk
1040:. It has led to a study of
3062:
2942:Extreme value theory (EVT)
2742:Doob decomposition theorem
2034:OrnsteinâUhlenbeck process
1805:Chinese restaurant process
1685:(2nd ed.). Springer.
1681:; Wellner, Jon A. (2000).
1485:10.1016/j.jspi.2006.02.016
26:
3010:
2822:Optional stopping theorem
2623:Large deviation principle
2375:HeathâJarrowâMorton (HJM)
2312:Moving-average (MA) model
2297:Autoregressive (AR) model
2122:Hidden Markov model (HMM)
2056:SchrammâLoewner evolution
1627:10.1007/978-0-387-74978-5
1587:The Annals of Probability
1452:GlivenkoâCantelli theorem
1054:GlivenkoâCantelli classes
623:converges in distribution
320:GlivenkoâCantelli theorem
64:non-parametric statistics
50:from its expectation. In
3046:Nonparametric statistics
2737:DolĂŠans-Dade exponential
2567:Progressively measurable
2365:CoxâIngersollâRoss (CIR)
1535:Billingsley, P. (1995).
1442:Khmaladze transformation
1064:As an example, consider
615:{\displaystyle G_{n}(A)}
18:Empirical process theory
2957:Mathematical statistics
2947:Large deviations theory
2777:Infinitesimal generator
2638:Maximal ergodic theorem
2557:Piecewise-deterministic
2159:Random dynamical system
2024:Markov additive process
1661:10.1137/1.9780898719017
1617:Kosorok, M. R. (2008).
1573:10.1214/aoms/1177729445
1554:Donsker, M. D. (1952).
1537:Probability and Measure
1517:10.1214/aoms/1177728852
1283:It has been shown that
2792:KarhunenâLoève theorem
2727:CameronâMartin formula
2691:BurkholderâDavisâGundy
2086:Variance gamma process
1608:Dudley, R. M. (1999).
1600:10.1214/aop/1176995384
1581:Dudley, R. M. (1978).
1498:Wolfowitz, J. (1954).
1410:
1368:
1301:
1277:
1206:
1026:
1000:
972:
905:
877:
802:
770:
745:
681:
680:{\displaystyle G_{n}f}
616:
573:
533:
411:
226:
177:
2922:Actuarial mathematics
2884:Uniform integrability
2879:Stratonovich integral
2807:LĂŠvyâProkhorov metric
2711:MarcinkiewiczâZygmund
2598:Central limit theorem
2200:Gaussian random field
2029:McKeanâVlasov process
1949:Dyson Brownian motion
1810:GaltonâWatson process
1679:van der Vaart, Aad W.
1411:
1369:
1302:
1278:
1207:
1027:
1001:
973:
906:
878:
803:
771:
746:
682:
617:
584:central limit theorem
574:
513:
412:
227:
157:
56:central limit theorem
2997:Time series analysis
2952:Mathematical finance
2837:Reflection principle
2164:Regenerative process
1964:FlemingâViot process
1779:Stochastic processes
1382:
1314:
1287:
1219:
1102:
1014:
986:
921:
891:
820:
780:
755:
691:
661:
590:
431:
335:
283:law of large numbers
122:
2992:Stochastic analysis
2832:Quadratic variation
2827:Prokhorov's theorem
2762:FeynmanâKac formula
2232:Markov random field
1880:Birthâdeath process
303:uniform convergence
2962:Probability theory
2842:Skorokhod integral
2812:Malliavin calculus
2395:Korn-Kreer-Lenssen
2279:Time series models
2242:PitmanâYor process
1714:10.1007/BF01239992
1406:
1364:
1297:
1273:
1202:
1095:they are given by
1068:. For real-valued
1022:
996:
968:
901:
873:
798:
766:
741:
677:
612:
569:
407:
252:For every (fixed)
243:indicator function
222:
60:empirical measures
44:stochastic process
36:probability theory
3041:Empirical process
3028:
3027:
2982:Signal processing
2701:Doob's upcrossing
2696:Doob's martingale
2660:EngelbertâSchmidt
2603:Donsker's theorem
2537:Feller-continuous
2405:RendlemanâBartter
2195:Dirichlet process
2112:Branching process
2081:Telegraph process
1974:Geometric process
1954:Empirical process
1944:Diffusion process
1800:Branching process
1795:Bernoulli process
1692:978-0-387-94640-5
1670:978-0-89871-684-9
1636:978-0-387-74977-8
1322:
1072:random variables
1038:Donsker's theorem
980:empirical process
885:empirical process
511:
496:
461:
365:
155:
52:mean field theory
40:empirical process
16:(Redirected from
3053:
3002:Machine learning
2889:Usual hypotheses
2772:Girsanov theorem
2757:Dynkin's formula
2522:Continuous paths
2430:Actuarial models
2370:GarmanâKohlhagen
2340:BlackâKarasinski
2335:BlackâDermanâToy
2322:Financial models
2188:Fields and other
2117:Gaussian process
2066:Sigma-martingale
1870:Additive process
1772:
1765:
1758:
1749:
1725:
1696:
1674:
1640:
1613:
1604:
1602:
1577:
1575:
1550:
1522:
1521:
1519:
1495:
1489:
1488:
1479:(9): 2733â2758.
1468:
1415:
1413:
1412:
1407:
1402:
1394:
1393:
1373:
1371:
1370:
1365:
1336:
1335:
1323:
1318:
1306:
1304:
1303:
1298:
1296:
1295:
1282:
1280:
1279:
1274:
1266:
1228:
1227:
1211:
1209:
1208:
1203:
1198:
1197:
1173:
1172:
1136:
1135:
1114:
1113:
1050:Gaussian process
1031:
1029:
1028:
1023:
1021:
1005:
1003:
1002:
997:
995:
994:
977:
975:
974:
969:
967:
966:
965:
964:
951:
950:
940:
939:
930:
929:
910:
908:
907:
902:
900:
899:
882:
880:
879:
874:
872:
871:
870:
869:
856:
855:
839:
838:
829:
828:
807:
805:
804:
799:
797:
796:
787:
775:
773:
772:
767:
762:
751:, provided that
750:
748:
747:
742:
737:
736:
724:
710:
686:
684:
683:
678:
673:
672:
641:)(1 â
629:random variable
621:
619:
618:
613:
602:
601:
578:
576:
575:
570:
568:
564:
560:
549:
548:
532:
527:
512:
504:
497:
492:
475:
474:
462:
457:
449:
448:
416:
414:
413:
408:
379:
378:
366:
361:
347:
346:
231:
229:
228:
223:
215:
214:
202:
201:
176:
171:
156:
148:
134:
133:
21:
3061:
3060:
3056:
3055:
3054:
3052:
3051:
3050:
3031:
3030:
3029:
3024:
3006:
2967:Queueing theory
2910:
2852:Skorokhod space
2715:
2706:KunitaâWatanabe
2677:
2643:Sanov's theorem
2613:Ergodic theorem
2586:
2582:Time-reversible
2500:
2463:Queueing models
2457:
2453:SparreâAnderson
2443:CramĂŠrâLundberg
2424:
2410:SABR volatility
2316:
2273:
2225:Boolean network
2183:
2169:Renewal process
2100:
2049:Non-homogeneous
2039:Poisson process
1929:Contact process
1892:Brownian motion
1862:Continuous time
1856:
1850:Maximal entropy
1781:
1776:
1732:
1699:
1693:
1677:
1671:
1643:
1637:
1616:
1607:
1580:
1553:
1547:
1534:
1531:
1529:Further reading
1526:
1525:
1497:
1496:
1492:
1470:
1469:
1465:
1460:
1438:
1418:Brownian bridge
1385:
1380:
1379:
1327:
1312:
1311:
1285:
1284:
1217:
1216:
1174:
1164:
1127:
1105:
1100:
1099:
1094:
1085:
1078:
1062:
1046:converge weakly
1042:Donsker classes
1012:
1011:
984:
983:
944:
931:
919:
918:
889:
888:
849:
830:
818:
817:
788:
778:
777:
753:
752:
728:
689:
688:
664:
659:
658:
593:
588:
587:
540:
502:
498:
466:
440:
429:
428:
370:
338:
333:
332:
313:
293:
264:
240:
206:
178:
125:
120:
119:
96:
87:
80:
72:
32:
23:
22:
15:
12:
11:
5:
3059:
3057:
3049:
3048:
3043:
3033:
3032:
3026:
3025:
3023:
3022:
3017:
3015:List of topics
3011:
3008:
3007:
3005:
3004:
2999:
2994:
2989:
2984:
2979:
2974:
2972:Renewal theory
2969:
2964:
2959:
2954:
2949:
2944:
2939:
2937:Ergodic theory
2934:
2929:
2927:Control theory
2924:
2918:
2916:
2912:
2911:
2909:
2908:
2907:
2906:
2901:
2891:
2886:
2881:
2876:
2871:
2870:
2869:
2859:
2857:Snell envelope
2854:
2849:
2844:
2839:
2834:
2829:
2824:
2819:
2814:
2809:
2804:
2799:
2794:
2789:
2784:
2779:
2774:
2769:
2764:
2759:
2754:
2749:
2744:
2739:
2734:
2729:
2723:
2721:
2717:
2716:
2714:
2713:
2708:
2703:
2698:
2693:
2687:
2685:
2679:
2678:
2676:
2675:
2656:BorelâCantelli
2645:
2640:
2635:
2630:
2625:
2620:
2615:
2610:
2605:
2600:
2594:
2592:
2591:Limit theorems
2588:
2587:
2585:
2584:
2579:
2574:
2569:
2564:
2559:
2554:
2549:
2544:
2539:
2534:
2529:
2524:
2519:
2514:
2508:
2506:
2502:
2501:
2499:
2498:
2493:
2488:
2483:
2478:
2473:
2467:
2465:
2459:
2458:
2456:
2455:
2450:
2445:
2440:
2434:
2432:
2426:
2425:
2423:
2422:
2417:
2412:
2407:
2402:
2397:
2392:
2387:
2382:
2377:
2372:
2367:
2362:
2357:
2352:
2347:
2342:
2337:
2332:
2326:
2324:
2318:
2317:
2315:
2314:
2309:
2304:
2299:
2294:
2289:
2283:
2281:
2275:
2274:
2272:
2271:
2266:
2261:
2260:
2259:
2254:
2244:
2239:
2234:
2229:
2228:
2227:
2222:
2212:
2210:Hopfield model
2207:
2202:
2197:
2191:
2189:
2185:
2184:
2182:
2181:
2176:
2171:
2166:
2161:
2156:
2155:
2154:
2149:
2144:
2139:
2129:
2127:Markov process
2124:
2119:
2114:
2108:
2106:
2102:
2101:
2099:
2098:
2096:Wiener sausage
2093:
2091:Wiener process
2088:
2083:
2078:
2073:
2071:Stable process
2068:
2063:
2061:Semimartingale
2058:
2053:
2052:
2051:
2046:
2036:
2031:
2026:
2021:
2016:
2011:
2006:
2004:Jump diffusion
2001:
1996:
1991:
1986:
1981:
1979:Hawkes process
1976:
1971:
1966:
1961:
1959:Feller process
1956:
1951:
1946:
1941:
1936:
1931:
1926:
1924:Cauchy process
1921:
1920:
1919:
1914:
1909:
1904:
1899:
1889:
1888:
1887:
1877:
1875:Bessel process
1872:
1866:
1864:
1858:
1857:
1855:
1854:
1853:
1852:
1847:
1842:
1837:
1827:
1822:
1817:
1812:
1807:
1802:
1797:
1791:
1789:
1783:
1782:
1777:
1775:
1774:
1767:
1760:
1752:
1746:
1745:
1739:
1731:
1730:External links
1728:
1727:
1726:
1697:
1691:
1675:
1669:
1649:Wellner, J. A.
1645:Shorack, G. R.
1641:
1635:
1614:
1605:
1593:(6): 899â929.
1578:
1566:(2): 277â281.
1551:
1545:
1530:
1527:
1524:
1523:
1490:
1462:
1461:
1459:
1456:
1455:
1454:
1449:
1444:
1437:
1434:
1433:
1432:
1405:
1401:
1397:
1392:
1388:
1363:
1360:
1357:
1354:
1351:
1348:
1345:
1342:
1339:
1334:
1330:
1326:
1321:
1294:
1272:
1269:
1265:
1261:
1258:
1255:
1252:
1249:
1246:
1243:
1240:
1237:
1234:
1231:
1226:
1213:
1212:
1201:
1196:
1193:
1190:
1187:
1184:
1181:
1177:
1171:
1167:
1163:
1160:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1134:
1130:
1126:
1123:
1120:
1117:
1112:
1108:
1090:
1083:
1076:
1061:
1058:
1034:
1033:
1020:
993:
963:
958:
955:
949:
943:
938:
934:
928:
916:
898:
868:
863:
860:
854:
848:
845:
842:
837:
833:
827:
795:
791:
786:
765:
761:
740:
735:
731:
727:
723:
719:
716:
713:
709:
705:
702:
699:
696:
676:
671:
667:
611:
608:
605:
600:
596:
580:
579:
567:
563:
559:
555:
552:
547:
543:
539:
536:
531:
526:
523:
520:
516:
510:
507:
501:
495:
490:
487:
484:
481:
478:
473:
469:
465:
460:
455:
452:
447:
443:
439:
436:
418:
417:
406:
403:
400:
397:
394:
391:
388:
385:
382:
377:
373:
369:
364:
359:
356:
353:
350:
345:
341:
327:signed measure
309:
289:
281:by the strong
260:
236:
233:
232:
221:
218:
213:
209:
205:
200:
197:
194:
191:
188:
185:
181:
175:
170:
167:
164:
160:
154:
151:
146:
143:
140:
137:
132:
128:
92:
85:
78:
71:
68:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3058:
3047:
3044:
3042:
3039:
3038:
3036:
3021:
3018:
3016:
3013:
3012:
3009:
3003:
3000:
2998:
2995:
2993:
2990:
2988:
2985:
2983:
2980:
2978:
2975:
2973:
2970:
2968:
2965:
2963:
2960:
2958:
2955:
2953:
2950:
2948:
2945:
2943:
2940:
2938:
2935:
2933:
2930:
2928:
2925:
2923:
2920:
2919:
2917:
2913:
2905:
2902:
2900:
2897:
2896:
2895:
2892:
2890:
2887:
2885:
2882:
2880:
2877:
2875:
2874:Stopping time
2872:
2868:
2865:
2864:
2863:
2860:
2858:
2855:
2853:
2850:
2848:
2845:
2843:
2840:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2813:
2810:
2808:
2805:
2803:
2800:
2798:
2795:
2793:
2790:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2763:
2760:
2758:
2755:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2733:
2730:
2728:
2725:
2724:
2722:
2718:
2712:
2709:
2707:
2704:
2702:
2699:
2697:
2694:
2692:
2689:
2688:
2686:
2684:
2680:
2673:
2669:
2665:
2664:HewittâSavage
2661:
2657:
2653:
2649:
2648:Zeroâone laws
2646:
2644:
2641:
2639:
2636:
2634:
2631:
2629:
2626:
2624:
2621:
2619:
2616:
2614:
2611:
2609:
2606:
2604:
2601:
2599:
2596:
2595:
2593:
2589:
2583:
2580:
2578:
2575:
2573:
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2553:
2550:
2548:
2545:
2543:
2540:
2538:
2535:
2533:
2530:
2528:
2525:
2523:
2520:
2518:
2515:
2513:
2510:
2509:
2507:
2503:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2472:
2469:
2468:
2466:
2464:
2460:
2454:
2451:
2449:
2446:
2444:
2441:
2439:
2436:
2435:
2433:
2431:
2427:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2401:
2398:
2396:
2393:
2391:
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2371:
2368:
2366:
2363:
2361:
2358:
2356:
2353:
2351:
2348:
2346:
2345:BlackâScholes
2343:
2341:
2338:
2336:
2333:
2331:
2328:
2327:
2325:
2323:
2319:
2313:
2310:
2308:
2305:
2303:
2300:
2298:
2295:
2293:
2290:
2288:
2285:
2284:
2282:
2280:
2276:
2270:
2267:
2265:
2262:
2258:
2255:
2253:
2250:
2249:
2248:
2247:Point process
2245:
2243:
2240:
2238:
2235:
2233:
2230:
2226:
2223:
2221:
2218:
2217:
2216:
2213:
2211:
2208:
2206:
2205:Gibbs measure
2203:
2201:
2198:
2196:
2193:
2192:
2190:
2186:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2160:
2157:
2153:
2150:
2148:
2145:
2143:
2140:
2138:
2135:
2134:
2133:
2130:
2128:
2125:
2123:
2120:
2118:
2115:
2113:
2110:
2109:
2107:
2103:
2097:
2094:
2092:
2089:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
2050:
2047:
2045:
2042:
2041:
2040:
2037:
2035:
2032:
2030:
2027:
2025:
2022:
2020:
2017:
2015:
2012:
2010:
2007:
2005:
2002:
2000:
1997:
1995:
1994:ItĂ´ diffusion
1992:
1990:
1987:
1985:
1982:
1980:
1977:
1975:
1972:
1970:
1969:Gamma process
1967:
1965:
1962:
1960:
1957:
1955:
1952:
1950:
1947:
1945:
1942:
1940:
1937:
1935:
1932:
1930:
1927:
1925:
1922:
1918:
1915:
1913:
1910:
1908:
1905:
1903:
1900:
1898:
1895:
1894:
1893:
1890:
1886:
1883:
1882:
1881:
1878:
1876:
1873:
1871:
1868:
1867:
1865:
1863:
1859:
1851:
1848:
1846:
1843:
1841:
1840:Self-avoiding
1838:
1836:
1833:
1832:
1831:
1828:
1826:
1825:Moran process
1823:
1821:
1818:
1816:
1813:
1811:
1808:
1806:
1803:
1801:
1798:
1796:
1793:
1792:
1790:
1788:
1787:Discrete time
1784:
1780:
1773:
1768:
1766:
1761:
1759:
1754:
1753:
1750:
1743:
1740:
1737:
1734:
1733:
1729:
1723:
1719:
1715:
1711:
1707:
1703:
1698:
1694:
1688:
1684:
1680:
1676:
1672:
1666:
1662:
1658:
1654:
1650:
1646:
1642:
1638:
1632:
1628:
1624:
1620:
1615:
1611:
1606:
1601:
1596:
1592:
1588:
1584:
1579:
1574:
1569:
1565:
1561:
1557:
1552:
1548:
1542:
1538:
1533:
1532:
1528:
1518:
1513:
1509:
1505:
1501:
1494:
1491:
1486:
1482:
1478:
1474:
1467:
1464:
1457:
1453:
1450:
1448:
1445:
1443:
1440:
1439:
1435:
1430:
1426:
1422:
1419:
1386:
1377:
1355:
1349:
1346:
1340:
1332:
1328:
1319:
1310:
1309:
1308:
1270:
1259:
1256:
1253:
1247:
1244:
1238:
1229:
1199:
1191:
1188:
1182:
1175:
1169:
1165:
1161:
1152:
1149:
1143:
1132:
1128:
1124:
1118:
1110:
1106:
1098:
1097:
1096:
1093:
1089:
1082:
1075:
1071:
1067:
1059:
1057:
1055:
1051:
1048:to a certain
1047:
1043:
1039:
1009:
981:
978:is called an
956:
953:
941:
936:
932:
917:
914:
886:
883:is called an
861:
858:
843:
835:
831:
816:
815:
814:
813:
809:
793:
789:
763:
733:
725:
717:
714:
703:
700:
694:
674:
669:
665:
656:
652:
648:
644:
640:
636:
632:
628:
624:
606:
598:
594:
585:
565:
561:
553:
545:
541:
534:
529:
524:
521:
518:
514:
508:
505:
499:
493:
488:
485:
479:
476:
471:
467:
458:
453:
450:
445:
441:
434:
427:
426:
425:
423:
398:
392:
389:
383:
375:
371:
362:
357:
351:
343:
339:
331:
330:
329:
328:
323:
321:
317:
312:
308:
304:
300:
297:
294:converges to
292:
288:
284:
280:
279:almost surely
276:
272:
268:
263:
259:
255:
250:
248:
244:
239:
219:
211:
207:
195:
192:
186:
179:
173:
168:
165:
162:
158:
152:
149:
144:
138:
130:
126:
118:
117:
116:
114:
110:
107:
103:
99:
95:
91:
84:
77:
69:
67:
65:
61:
57:
53:
49:
45:
41:
37:
30:
19:
2932:Econometrics
2894:Wiener space
2782:ItĂ´ integral
2683:Inequalities
2572:Self-similar
2542:GaussâMarkov
2532:Exchangeable
2512:CĂ dlĂ g paths
2448:Risk process
2400:LIBOR market
2269:Random graph
2264:Random field
2076:Superprocess
2014:LĂŠvy process
2009:Jump process
1984:Hunt process
1953:
1820:Markov chain
1705:
1701:
1682:
1652:
1618:
1609:
1590:
1586:
1563:
1559:
1536:
1507:
1503:
1493:
1476:
1472:
1466:
1428:
1424:
1420:
1214:
1091:
1087:
1080:
1073:
1063:
1035:
1007:
979:
912:
884:
811:
810:
654:
650:
646:
642:
638:
634:
630:
581:
421:
419:
324:
315:
310:
306:
295:
290:
286:
274:
270:
266:
261:
257:
253:
251:
246:
237:
234:
112:
108:
104:with common
101:
93:
89:
82:
75:
73:
39:
33:
2977:Ruin theory
2915:Disciplines
2787:ItĂ´'s lemma
2562:Predictable
2237:Percolation
2220:Potts model
2215:Ising model
2179:White noise
2137:Differences
1999:ItĂ´ process
1939:Cox process
1835:Loop-erased
1830:Random walk
1708:(3): 2147.
1510:: 131â138.
982:indexed by
887:indexed by
285:. That is,
245:of the set
3035:Categories
2987:Statistics
2767:Filtration
2668:Kolmogorov
2652:Blumenthal
2577:Stationary
2517:Continuous
2505:Properties
2390:HullâWhite
2132:Martingale
2019:Local time
1907:Fractional
1885:pure birth
1546:0471007102
1458:References
1374:converges
812:Definition
70:Definition
2899:Classical
1912:Geometric
1902:Excursion
1722:123206522
1391:∞
1387:ℓ
1347:−
1260:∈
1242:∞
1239:−
1186:∞
1183:−
1147:∞
1144:−
957:∈
862:∈
718:−
633:(0,
554:−
515:∑
477:−
438:↦
424:given by
390:−
299:pointwise
190:∞
187:−
159:∑
3020:Category
2904:Abstract
2438:BĂźhlmann
2044:Compound
1651:(2009).
1436:See also
2527:Ergodic
2415:VaĹĄĂÄek
2257:Poisson
1917:Meander
1086:, ...,
1060:Example
808:exist.
582:By the
318:by the
241:is the
235:where I
2867:Tanaka
2552:Mixing
2547:Markov
2420:Wilkie
2385:HoâLee
2380:Heston
2152:Super-
1897:Bridge
1845:Biased
1720:
1689:
1667:
1633:
1543:
1376:weakly
627:normal
88:, ...
2720:Tools
2496:M/M/c
2491:M/M/1
2486:M/G/1
2476:Fluid
2142:Local
1718:S2CID
1416:to a
625:to a
42:is a
38:, an
2672:LĂŠvy
2471:Bulk
2355:Chen
2147:Sub-
2105:Both
1687:ISBN
1665:ISBN
1631:ISBN
1541:ISBN
1431:)) .
776:and
74:For
58:for
2252:Cox
1710:doi
1657:doi
1623:doi
1595:doi
1568:doi
1512:doi
1481:doi
1477:137
1378:in
1070:iid
1010:to
314:to
305:of
100:in
34:In
3037::
2670:,
2666:,
2662:,
2658:,
2654:,
1716:.
1706:20
1704:.
1663:.
1655:.
1647:;
1629:.
1589:.
1585:.
1564:23
1562:.
1558:.
1508:25
1506:.
1502:.
1475:.
1079:,
657:,
586:,
322:.
277:)
256:,
249:.
81:,
66:.
2674:)
2650:(
1771:e
1764:t
1757:v
1724:.
1712::
1695:.
1673:.
1659::
1639:.
1625::
1603:.
1597::
1591:6
1576:.
1570::
1549:.
1520:.
1514::
1487:.
1483::
1429:x
1427:(
1425:F
1423:(
1421:B
1404:)
1400:R
1396:(
1362:)
1359:)
1356:x
1353:(
1350:F
1344:)
1341:x
1338:(
1333:n
1329:F
1325:(
1320:n
1293:C
1271:.
1268:}
1264:R
1257:x
1254::
1251:]
1248:x
1245:,
1236:(
1233:{
1230:=
1225:C
1200:.
1195:]
1192:x
1189:,
1180:(
1176:I
1170:n
1166:P
1162:=
1159:)
1156:]
1153:x
1150:,
1141:(
1138:(
1133:n
1129:P
1125:=
1122:)
1119:x
1116:(
1111:n
1107:F
1092:n
1088:X
1084:2
1081:X
1077:1
1074:X
1032:.
1019:R
1008:S
992:F
962:F
954:f
948:)
942:f
937:n
933:G
927:(
915:.
913:S
897:C
867:C
859:c
853:)
847:)
844:c
841:(
836:n
832:G
826:(
794:2
790:f
785:E
764:f
760:E
739:)
734:2
730:)
726:f
722:E
715:f
712:(
708:E
704:,
701:0
698:(
695:N
675:f
670:n
666:G
655:f
651:A
647:A
645:(
643:P
639:A
637:(
635:P
631:N
610:)
607:A
604:(
599:n
595:G
566:)
562:f
558:E
551:)
546:i
542:X
538:(
535:f
530:n
525:1
522:=
519:i
509:n
506:1
500:(
494:n
489:=
486:f
483:)
480:P
472:n
468:P
464:(
459:n
454:=
451:f
446:n
442:G
435:f
422:f
405:)
402:)
399:A
396:(
393:P
387:)
384:A
381:(
376:n
372:P
368:(
363:n
358:=
355:)
352:A
349:(
344:n
340:G
316:F
311:n
307:F
296:F
291:n
287:F
275:x
273:(
271:F
267:x
265:(
262:n
258:F
254:x
247:C
238:C
220:,
217:)
212:i
208:X
204:(
199:]
196:x
193:,
184:(
180:I
174:n
169:1
166:=
163:i
153:n
150:1
145:=
142:)
139:x
136:(
131:n
127:F
113:x
111:(
109:F
102:R
94:n
90:X
86:2
83:X
79:1
76:X
31:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.