Knowledge (XXG)

Skorokhod problem

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Haddad, J. P.; Mazumdar, R. R.; Piera, F. J. (2010). "Pathwise comparison results for stochastic fluid networks".
433: 316: 294: 264: 32: 17: 417: 382: 373: 351: 276: 340:"Stochastic differential equations with reflecting boundary condition in convex regions" 460: 82:), t ≥ 0} are said to solve the Skorokhod problem if for all non-negative 48: 339: 267:(1984). "Stochastic differential equations with reflecting boundary conditions". 413: 405: 386: 356: 319:(1962). "Stochastic equations for diffusion processes in a bounded region 2". 297:(1961). "Stochastic equations for diffusion processes in a bounded region 1". 35:
who first published the solution to a stochastic differential equation for a
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The classic version of the problem states that given a
135: 202: 269:Communications on Pure and Applied Mathematics 441: 244:List of things named after Anatoliy Skorokhod 8: 448: 434: 355: 218:is often known as the reflection matrix, 179: 170: 155: 145: 140: 134: 255: 28:with a reflecting boundary condition. 7: 402: 400: 420:. You can help Knowledge (XXG) by 14: 404: 26:stochastic differential equation 226:) as the reflected process and 321:Theor. Veroyatnost. I Primenen 299:Theor. Veroyatnost. I Primenen 191: 185: 167: 161: 1: 66:, then stochastic processes { 234:) as the regulator process. 24:is the problem of solving a 59:), t ≥ 0} and an 31:The problem is named after 488: 399: 37:reflecting Brownian motion 387:10.1007/s11134-010-9187-9 74:), t ≥ 0} and { 338:Tanaka, Hiroshi (1979). 357:10.32917/hmj/1206135203 119:(0) = 0 and d 416:-related article is a 281:10.1002/cpa.3160370408 204: 205: 133: 467:Stochastic calculus 150: 200: 136: 33:Anatoliy Skorokhod 18:probability theory 472:Probability stubs 429: 428: 344:Hiroshima Math. J 173: 43:Problem statement 22:Skorokhod problem 479: 450: 443: 436: 408: 401: 391: 390: 374:Queueing Systems 368: 362: 361: 359: 335: 329: 328: 317:Skorokhod, A. V. 313: 307: 306: 295:Skorokhod, A. V. 291: 285: 284: 260: 209: 207: 206: 201: 184: 183: 174: 171: 160: 159: 149: 144: 487: 486: 482: 481: 480: 478: 477: 476: 457: 456: 455: 454: 397: 395: 394: 370: 369: 365: 337: 336: 332: 315: 314: 310: 293: 292: 288: 265:Sznitman, A. S. 262: 261: 257: 252: 240: 175: 151: 131: 130: 127:) ≥ 0 113:) ≥ 0 45: 12: 11: 5: 485: 483: 475: 474: 469: 459: 458: 453: 452: 445: 438: 430: 427: 426: 409: 393: 392: 363: 350:(1): 163–177. 330: 308: 286: 263:Lions, P. L.; 254: 253: 251: 248: 247: 246: 239: 236: 212: 211: 199: 196: 193: 190: 187: 182: 178: 169: 166: 163: 158: 154: 148: 143: 139: 128: 114: 105:) +  97:) =  44: 41: 13: 10: 9: 6: 4: 3: 2: 484: 473: 470: 468: 465: 464: 462: 451: 446: 444: 439: 437: 432: 431: 425: 423: 419: 415: 410: 407: 403: 398: 388: 384: 380: 376: 375: 367: 364: 358: 353: 349: 345: 341: 334: 331: 326: 322: 318: 312: 309: 304: 300: 296: 290: 287: 282: 278: 274: 270: 266: 259: 256: 249: 245: 242: 241: 237: 235: 233: 229: 225: 221: 217: 197: 194: 188: 180: 176: 164: 156: 152: 146: 141: 137: 129: 126: 122: 118: 115: 112: 108: 104: 100: 96: 92: 89: 88: 87: 85: 81: 77: 73: 69: 65: 62: 58: 54: 50: 42: 40: 38: 34: 29: 27: 23: 19: 422:expanding it 411: 396: 378: 372: 366: 347: 343: 333: 324: 320: 311: 302: 298: 289: 272: 268: 258: 231: 227: 223: 219: 215: 213: 124: 120: 116: 110: 106: 102: 98: 94: 90: 83: 79: 75: 71: 67: 63: 56: 52: 46: 30: 21: 15: 414:probability 214:The matrix 461:Categories 381:(2): 155. 305:: 264–274. 275:(4): 511. 250:References 138:∫ 51:process { 238:See also 86:values, 61:M-matrix 327:: 3–23. 49:càdlàg 20:, the 412:This 418:stub 383:doi 352:doi 277:doi 107:R Z 16:In 463:: 379:66 377:. 346:. 342:. 323:. 301:. 273:37 271:. 39:. 449:e 442:t 435:v 424:. 389:. 385:: 360:. 354:: 348:9 325:7 303:6 283:. 279:: 232:t 230:( 228:Z 224:t 222:( 220:W 216:R 210:. 198:0 195:= 192:) 189:s 186:( 181:i 177:Z 172:d 168:) 165:s 162:( 157:i 153:W 147:t 142:0 125:t 123:( 121:Z 117:Z 111:t 109:( 103:t 101:( 99:X 95:t 93:( 91:W 84:t 80:t 78:( 76:Z 72:t 70:( 68:W 64:R 57:t 55:( 53:X

Index

probability theory
stochastic differential equation
Anatoliy Skorokhod
reflecting Brownian motion
càdlàg
M-matrix
List of things named after Anatoliy Skorokhod
Sznitman, A. S.
doi
10.1002/cpa.3160370408
Skorokhod, A. V.
Skorokhod, A. V.
"Stochastic differential equations with reflecting boundary condition in convex regions"
doi
10.32917/hmj/1206135203
Queueing Systems
doi
10.1007/s11134-010-9187-9
Stub icon
probability
stub
expanding it
v
t
e
Categories
Stochastic calculus
Probability stubs

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