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Tilted large deviation principle

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25: 348: 462: 639: 252: 379: 42: 89: 61: 68: 75: 501: 57: 668: 108: 708: 698: 46: 82: 703: 660: 693: 343:{\displaystyle J_{\varepsilon }(S)=\int _{S}e^{F(x)/\varepsilon }\,\mathrm {d} \mu _{\varepsilon }(x)} 149: 126: 35: 177: 678: 146: 457:{\displaystyle \nu _{\varepsilon }(S)={\frac {J_{\varepsilon }(S)}{J_{\varepsilon }(X)}}.} 8: 231: 153: 138: 664: 200: 180: 656: 235: 675: 173: 687: 208: 134: 169: 122: 24: 142: 634:{\displaystyle I^{F}(x)=\sup _{y\in X}{\big }-{\big }.} 504: 382: 255: 152:. It can be seen as an alternative formulation of 49:. Unsourced material may be challenged and removed. 633: 456: 342: 207:that satisfies the large deviation principle with 353:and define a new family of probability measures ( 685: 528: 133:is a result that allows one to generate a new 650: 623: 589: 579: 545: 483:satisfies the large deviation principle on 159: 315: 109:Learn how and when to remove this message 686: 47:adding citations to reliable sources 18: 13: 317: 58:"Tilted large deviation principle" 14: 720: 238:from above. For each Borel set 131:tilted large deviation principle 23: 659:Monographs 14. Providence, RI: 34:needs additional citations for 618: 612: 603: 597: 574: 568: 559: 553: 521: 515: 445: 439: 424: 418: 399: 393: 337: 331: 302: 296: 272: 266: 1: 661:American Mathematical Society 651:den Hollander, Frank (2000). 644: 495: →  given by 7: 10: 725: 218: → . Let 135:large deviation principle 125:— specifically, in 160:Statement of the theorem 709:Large deviations theory 699:Mathematical principles 127:large deviations theory 635: 458: 344: 636: 459: 345: 178:completely metrizable 704:Probability theorems 502: 380: 253: 201:probability measures 43:improve this article 16:Mathematical formula 694:Asymptotic analysis 487:with rate function 242: ⊆  232:continuous function 226: →  139:exponential tilting 137:from an old one by 663:. pp. x+143. 631: 542: 454: 340: 527: 449: 181:topological space 119: 118: 111: 93: 716: 674: 657:Fields Institute 653:Large deviations 640: 638: 637: 632: 627: 626: 593: 592: 583: 582: 549: 548: 541: 514: 513: 463: 461: 460: 455: 450: 448: 438: 437: 427: 417: 416: 406: 392: 391: 349: 347: 346: 341: 330: 329: 320: 314: 313: 309: 287: 286: 265: 264: 154:Varadhan's lemma 114: 107: 103: 100: 94: 92: 51: 27: 19: 724: 723: 719: 718: 717: 715: 714: 713: 684: 683: 671: 647: 622: 621: 588: 587: 578: 577: 544: 543: 531: 509: 505: 503: 500: 499: 482: 475: 433: 429: 428: 412: 408: 407: 405: 387: 383: 381: 378: 377: 368: 361: 325: 321: 316: 305: 292: 288: 282: 278: 260: 256: 254: 251: 250: 199:be a family of 198: 191: 162: 115: 104: 98: 95: 52: 50: 40: 28: 17: 12: 11: 5: 722: 712: 711: 706: 701: 696: 682: 681: 669: 646: 643: 642: 641: 630: 625: 620: 617: 614: 611: 608: 605: 602: 599: 596: 591: 586: 581: 576: 573: 570: 567: 564: 561: 558: 555: 552: 547: 540: 537: 534: 530: 526: 523: 520: 517: 512: 508: 477: 471: 465: 464: 453: 447: 444: 441: 436: 432: 426: 423: 420: 415: 411: 404: 401: 398: 395: 390: 386: 363: 357: 351: 350: 339: 336: 333: 328: 324: 319: 312: 308: 304: 301: 298: 295: 291: 285: 281: 277: 274: 271: 268: 263: 259: 193: 187: 161: 158: 117: 116: 31: 29: 22: 15: 9: 6: 4: 3: 2: 721: 710: 707: 705: 702: 700: 697: 695: 692: 691: 689: 680: 677: 672: 670:0-8218-1989-5 666: 662: 658: 654: 649: 648: 628: 615: 609: 606: 600: 594: 584: 571: 565: 562: 556: 550: 538: 535: 532: 524: 518: 510: 506: 498: 497: 496: 494: 491: :  490: 486: 480: 474: 470: 451: 442: 434: 430: 421: 413: 409: 402: 396: 388: 384: 376: 375: 374: 372: 366: 360: 356: 334: 326: 322: 310: 306: 299: 293: 289: 283: 279: 275: 269: 261: 257: 249: 248: 247: 245: 241: 237: 233: 229: 225: 222: :  221: 217: 214: :  213: 210: 209:rate function 206: 202: 196: 190: 186: 182: 179: 175: 171: 167: 157: 155: 151: 148: 144: 140: 136: 132: 128: 124: 113: 110: 102: 91: 88: 84: 81: 77: 74: 70: 67: 63: 60: –  59: 55: 54:Find sources: 48: 44: 38: 37: 32:This article 30: 26: 21: 20: 652: 492: 488: 484: 478: 472: 468: 466: 370: 364: 358: 354: 352: 243: 239: 227: 223: 219: 215: 211: 204: 194: 188: 184: 183:), and let ( 170:Polish space 165: 163: 130: 129:— the 120: 105: 96: 86: 79: 72: 65: 53: 41:Please help 36:verification 33: 147:exponential 145:against an 143:integration 123:mathematics 688:Categories 645:References 150:functional 69:newspapers 607:− 585:− 563:− 536:∈ 435:ε 414:ε 389:ε 385:ν 327:ε 323:μ 311:ε 280:∫ 262:ε 174:separable 172:(i.e., a 99:June 2021 234:that is 679:1739680 236:bounded 141:, i.e. 83:scholar 667:  479:ε 473:ε 469:ν 467:Then ( 365:ε 359:ε 355:ν 246:, let 195:ε 189:ε 185:μ 85:  78:  71:  64:  56:  481:>0 367:>0 230:be a 197:>0 168:be a 90:JSTOR 76:books 665:ISBN 164:Let 62:news 529:sup 373:by 369:on 203:on 121:In 45:by 690:: 676:MR 655:. 176:, 156:. 673:. 629:. 624:] 619:) 616:x 613:( 610:I 604:) 601:x 598:( 595:F 590:[ 580:] 575:) 572:y 569:( 566:I 560:) 557:y 554:( 551:F 546:[ 539:X 533:y 525:= 522:) 519:x 516:( 511:F 507:I 493:X 489:I 485:X 476:) 452:. 446:) 443:X 440:( 431:J 425:) 422:S 419:( 410:J 403:= 400:) 397:S 394:( 371:X 362:) 338:) 335:x 332:( 318:d 307:/ 303:) 300:x 297:( 294:F 290:e 284:S 276:= 273:) 270:S 267:( 258:J 244:X 240:S 228:R 224:X 220:F 216:X 212:I 205:X 192:) 166:X 112:) 106:( 101:) 97:( 87:· 80:· 73:· 66:· 39:.

Index


verification
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adding citations to reliable sources
"Tilted large deviation principle"
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scholar
JSTOR
Learn how and when to remove this message
mathematics
large deviations theory
large deviation principle
exponential tilting
integration
exponential
functional
Varadhan's lemma
Polish space
separable
completely metrizable
topological space
probability measures
rate function
continuous function
bounded
Fields Institute
American Mathematical Society
ISBN

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