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Revuz D., Yor M. — Continuous martingales and Brownian motion
Revuz D., Yor M. — Continuous martingales and Brownian motion



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Название: Continuous martingales and Brownian motion

Авторы: Revuz D., Yor M.

Аннотация:

From the reviews: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. . . . This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research. . . " Bull. L. M. S. 24, 4 (1992) Since the first edition in 1990, an impressive variety of advances has been made in relation to the material found in this book.


Язык: en

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1999

Количество страниц: 602

Добавлена в каталог: 12.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Polarity for the Brownian sheet      198
Polarization      124
Potential kernel      100
Predictable      47
Predictable $\sigma$-field      47 171
Predictable process      171
Predictable projection      173
Predictable representation property      209
Predictable stopping      76
Predictable stopping time      172
Principal values for Brownian local times      236
Progressively measurable process      44
Prokhorov' s criterion      10 516
Pseudo-Brownian bridge      248
Pure local martingales      212
Pure martingales      212
Quadratic variation      28
Quadratic variation of Brownian motion      29
Quadratic variation of local mart      124
Quadratic variation of semimarts      128
Quasi-invariance of Wiener measure      339
Quasi-left continuity      101
Quasi-martingales      134
Ray — Knight theorems      454
Ray — Knight theorems for local times of Bessel processes      459
Recurrence of Brownian motion      58 192
Recurrent process      424
Recurrent set      424
Reduced Gaussian random variable      11
Reflecting brownian motion      86 239
Reflection principle      105
Regular linear Markov process      300
Regular points      98
Reproducing kernel Hilbert space      21 39 339
Resolvent equation      89
Right-continuous filtration      42
Scale function      302
Scale function of Bessel processes      442 446
Scaling invariance of Bessel process      446
Scaling invariance of Brownian motion      21
Scaling invariance of local time      244
Second arcsine law      242
Section theorem      172
Semimartingale      127
Semimartingale functions of BM      419
Sheet, Brownian      39
Signed-additive functional      419
Size of a OU process      37
Skew Brownian motion      292
Skew-product      194
Skew-product representation of Brownian motion      194
Skorokhod's lemma      239
Slowly reflecting      307
Solutions to linear SDE's      378 381
Space-time Markov process      85
Speed measure      304
Squared Bessel bridge      463
Squared Bessel process      440
Stable process      116
Stable process, symmetric      116
Stable random variable      115
Stable subspace of $H_{0}^{2}$      174
Standard Brownian motion      19 97
Standard local martingale      213
Standard local martingales      213
State space      15
Stationary independent increments      96
Stationary process      36
Stochastic area      196 396
Stochastic differential equation      366
Stochastic differential equation with reflection      385
Stochastic integral      138 140 141
Stochastic process      15
Stopped process      44
Stopping time      42
Strassen's law of the iterated logarithm      346
Stratonovitch integral      144
Strong additive functional      402
Strong Markov property      102
Strong Markov property, extended      111
Strong solution      367
Submarkovian      84
Submartingales      51
Subordinator      117
Supermartingale      51
Support of local times      235
Symmetric local times      234
Symmetric stable processes      116
Tanaka, Ito — Tanaka formula      223
Terminal time      491
The intervals of constancy are the same for a continuous local martingale and for its bracket      125
The planar Brownian curve: its Lebesgue measure is zero      23 196
The time spent by the Brownian Bridge on the positive half-line is uniformly distributed      493
Time change      180
Time inversion      359
Time reversal      312
Times at which the BM is equal to its supremum      113
Transient process      424
Transient set      424
Transition function      80
Transition probability      80
Trap      97
Tsirel'son's example      392
Uniqueness in law      367
Upcrossings      60
Usual augmentation of a filtration      45
Variation      5
Variation, p-variation of BM      33
Vector, local martingale, semimartingale      147
Ventcell — Freidlin estimates      343
Version      18
Watanabe's process      504
Weak convergence      10
Weak solution to a stochastic differential equation      367
Wiener Chaos      201 207
Wiener measure      35
Wiener space      35
Williams description of Ito's measure      499
Williams path decomposition theorem      318
Zvonkin method      384
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