Diffusions, Markov Processes, and Martingales: Itô calculusThis celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science. |
Contents
II | 1 |
III | 2 |
V | 4 |
VI | 8 |
VII | 9 |
VIII | 10 |
IX | 11 |
X | 14 |
LXXXIV | 239 |
LXXXV | 246 |
LXXXVI | 250 |
LXXXVII | 263 |
LXXXVIII | 265 |
LXXXIX | 266 |
XC | 267 |
XCI | 269 |
XII | 15 |
XIII | 16 |
XIV | 17 |
XV | 18 |
XVI | 20 |
XVII | 21 |
XVIII | 23 |
XIX | 24 |
XX | 25 |
XXI | 27 |
XXII | 29 |
XXIII | 30 |
XXIV | 33 |
XXV | 37 |
XXVI | 42 |
XXVII | 45 |
XXVIII | 46 |
XXIX | 47 |
XXX | 50 |
XXXI | 52 |
XXXII | 57 |
XXXIII | 58 |
XXXIV | 63 |
XXXV | 64 |
XXXVI | 69 |
XXXVII | 73 |
XXXVIII | 75 |
XXXIX | 79 |
XL | 83 |
XLI | 86 |
XLII | 89 |
XLIII | 93 |
XLIV | 95 |
XLV | 99 |
XLVI | 102 |
XLVII | 106 |
XLVIII | 108 |
XLIX | 110 |
L | 112 |
LI | 113 |
LII | 114 |
LIV | 117 |
LV | 119 |
LVI | 122 |
LVII | 124 |
LVIII | 125 |
LIX | 128 |
LX | 132 |
LXI | 136 |
LXII | 141 |
LXIII | 144 |
LXIV | 149 |
LXV | 151 |
LXVI | 155 |
LXVII | 158 |
LXVIII | 160 |
LXIX | 162 |
LXX | 163 |
LXXI | 166 |
LXXII | 170 |
LXXIII | 173 |
LXXIV | 175 |
LXXV | 177 |
LXXVI | 178 |
LXXVII | 181 |
LXXVIII | 182 |
LXXIX | 186 |
LXXX | 193 |
LXXXI | 198 |
LXXXII | 203 |
LXXXIII | 224 |
XCII | 270 |
XCIII | 271 |
XCIV | 273 |
XCV | 276 |
XCVI | 284 |
XCVII | 289 |
XCVIII | 291 |
XCIX | 295 |
C | 297 |
CI | 300 |
CII | 301 |
CIII | 304 |
CIV | 308 |
CV | 313 |
CVI | 315 |
CVII | 317 |
CVIII | 318 |
CIX | 319 |
CX | 322 |
CXI | 327 |
CXII | 329 |
CXIII | 331 |
CXIV | 332 |
CXV | 334 |
CXVI | 336 |
CXVII | 338 |
CXVIII | 340 |
CXIX | 343 |
CXX | 346 |
CXXI | 347 |
CXXII | 349 |
CXXIII | 350 |
CXXIV | 352 |
CXXV | 354 |
CXXVI | 358 |
CXXVII | 359 |
CXXVIII | 360 |
CXXIX | 361 |
CXXX | 364 |
CXXXI | 367 |
CXXXII | 369 |
CXXXIII | 372 |
CXXXIV | 374 |
CXXXV | 375 |
CXXXVI | 376 |
CXXXVII | 377 |
CXXXVIII | 382 |
CXXXIX | 388 |
CXL | 391 |
CXLI | 394 |
CXLIII | 398 |
CXLIV | 400 |
CXLV | 405 |
CXLVI | 406 |
CXLVII | 410 |
CXLVIII | 413 |
CXLIX | 416 |
CL | 418 |
CLI | 420 |
CLII | 425 |
CLIII | 428 |
CLIV | 431 |
CLV | 432 |
CLVI | 433 |
CLVII | 438 |
CLVIII | 439 |
CLIX | 442 |
CLX | 445 |
449 | |
469 | |
Other editions - View all
Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus L. C. G. Rogers,David Williams No preview available - 2000 |
Common terms and phrases
1-dimensional diffusion adapted R-process applications B₁ bounded previsible Brownian motion calculus continuous local martingale continuous semimartingale coordinates define definition Dellacherie denote density diffeomorphism Doléans dual previsible projection example Exercise exists exponential filtration finite variation finite-variation follows function Hence increasing process independent Itô calculus Itô's formula Lemma Lévy Lévy process Lipschitz local martingale Malliavin calculus manifold Markov process Markov property martingale null martingale problem matrix metric Meyer decomposition notation o-algebra orthogonal orthonormal path pathwise uniqueness PCHAF Poisson previsible process previsible stopping prove R-process random variable result Riemannian satisfies semimartingale sequence set-up smooth space Stieltjes integral stochastic integral Stratonovich submartingale supermartingale Suppose T₁ Tanaka's formula tangent vector Theorem uniformly integrable uniformly integrable martingale uniqueness in law vector fields Watanabe weak solution X₁ Y₁