Revuz D., Yor M. — Continuous martingales and Brownian motion :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

Предметный указатель

$L^{p}$ -inequalities for local times      265
$\sigma$ -discrete point process      471
$\sigma$ -integrable additive functional      410
( $\mathcal{F}_{t}$ ) brownian motion      97
A 0-1 law for additive functionals of BM      422
A bounded ( $\mathcal{F}_{t}^{B}$ )-martingale which is the stochastic integral of an unbounded process of $L^{2}(B)$       269
A Brownian filtration sandwiched between $\mathcal{F}^{B}$ and $\mathcal{F}^{|B|}$       208
A Fourier transform proof of the existence of occupation densities      166
A Girsanov transform of a BM with a strictly smaller filtration      397
A Girsanov transform of a pure martingale which is not pure      393
A local martingale is Gaussian iff its bracket is deterministic      186
A local martingale with strong integrability properties is not necessarily a martingale      194
A progressive set which is not optional      175
A semimartingale X = M + A such that $\mathcal{F}^{X} \subset \mathcal{F}^{M}$ strictly      259
A slowly reflecting boundary      421
A uniformly integrable martingale which is not in $H^{1}$       75
Absorbing point      84 97
Action functional      342
Adapted process      42
Additive functional      401
Additivity property of squared Bessel processes      440
An exponential local martingale which is not a martingale      335
An extremal martingale which is not pure      214
Approximations of $L_{t}$ and $S_{t}$       227 233
Associativity of stochastic integrals      139
Asymptotic $\sigma$ -field      99
Asymptotic properties for the transition function of the Brownian motion      100
Asymptotic version of Knight's      524
atom      76
Bachelier's equation      268
Backward equation      282
Backward integral      144
Bernstein inequality      153
Bernstein's inequality      153
Bessel bridge      463
Bessel bridges      463
Bessel processes      445
Bismut description of Ito's measure      502
Blumenthal zero one law      95
BMO-martingales      75
Bougerol's identity      388
Bracket of two continuous local martingales      125
Bracket of two semimartingales      128
Brownian bridge      37 154 384
Brownian bridge as conditioned Brownian motion      41
Brownian excursion      480
Brownian meander      493
Brownian motion      19
Brownian motion on the sphere      530
Brownian motion with drift      73 352
Brownian sheet      39
Burkholder — Davis — Gundy inequalities      160
Burkholder — Davis — Gundy inequality      160
Cadlag      34
Cadlag process      34
Cameron — Martin formula      371 445
Cameron — Martin space      339
Canonical process      34
Canonical realization      92
Cauchy process      116
Cauchy r.v.      13
Cemetery      84
Central-limit theorem for stochastic integrals      160
Chacon — Ornstein theorem      548
Chain rule      6
Chaos, Wiener      201 207
Chapman — Kolmogorov equation      80
Characteristic measure of a Poisson point process      475
Chernov inequality      292
Chung — Jacobi — Riemann identity      509
Clark's formula      341
Comparison theorems      393
Complete filtration      45
Conditioning with respect to last exit times      408
Conformal invariance of Brownian motion      190
Conformal local martingale      189
Conformal local martingales      189
Continuous additive functional      401
Continuous local martingales on $]0, \infty[$       135 157
Continuous local martingales on stochastic intervals      136
Continuous process      17
Convergence in distribution      516
Convergence in law      10
Convergence in the sense of finite dimensional distributions      516
Convergence in the sense of finite distributions      516
Cooptional time      313
Covariance      294
Cramer transform      343
Criterions for an exponential local martingale to be a martingale      331 332 338
d-dimensional brownian      20
d-dimensional Ornstein — Uhlenbeck process      360
Dambis      181
Debut      46
Deterministic semimartingales are functions of bounded variation      133 145
Deviations of Brownian motion, large deviations      345
Differentiability of BM, non differentiability      32
Differentiation of stochastic integrals      143
Diffusion coefficient      294
Diffusion process      294
Discontinuous local time for a diffusion      420
Discontinuous local time for a semimartingale      238
Discrete P.P.      471
Discrete point process      471
Discrete, $\sigma$ -discrete P.P.      471
Distribution, convergence in distribution      516
Dominated process      162
Donsker's theorem      518
Doob's inequality      54
Doss — Suessmann method      382
Downcrossings      60
Drift coefficient      294
Drift, Brownian motion with drift      73 352
Dubins inequality      66
Dubins — Schwarz      181
Dynkin's operator      310
Elastic BM      408
Energy      527
Enlargement of a filtration      363
Enlargement of a probability space      182
Entrance boundary      305 395
Entrance law      494
Entry time      43
Ergodic theorem      427 548
Ergodic theorem for BM      548
Exceptional points for the law of the iterated logarithm      59
Excessive function      423
Excessive measure      409
Excursions intervals      109
Excursions process      480
Explosions, criterion for explosions      383
Exponential formulas      476
Exponential holding point      97
Exponential holding time      97
Exponential inequality      153
Exponential local martingales      148
Exponentials of semimartingales      149
Extended infinitesimal generator      285
Extremal martingales      213
Extremal probability measures      210
Extremal process      406
Fefferman inequality      76
Fefferman's inequality      76
Feller process      90
Feller property, strong      423
Feller semi-groups      88
Feynman — Kac formula      358
Filtered space      41
Filtering      175 207
Filtration      41
Fine topology      98

Finite dimensional distributions      18
Finite dimensional distributions of BM      23
Finite variation process      119
Finite-variation process      119
First arcsine law      112
Fokker — Planck equation      282
Forward equation      282
Fractional Brownian motion      38
Fubini's Theorem for stochastic integrals      175
Functions of the BM which are martingales      74
Galmarino's test      47
Garsia — Neveu lemma      170
Gaussian Markov process      86
Gaussian martingales      133 186
Gaussian measure      16
Gaussian process      36
Gaussian random variable      11
Gaussian space      12
Gebelein inequality      205
Gebelein's inequality      205
Girsanov pair      329
Girsanov theorem      327
Girsanov transformation      329
Good $\lambda$ inequality      164
Gronwall's lemma      543
Hardy's inequality      75 155
Harris recurrent      425
Hausdorff dimension of the set of zeros of Brownian motion      247
Heat process      20
Hermite polynomials      151
Hitting time      43
Hoelder properties of BM      28 30
Hoelder properties of local times      237
Hoelder properties of semimarts      187
Holding point      97
Homogeneous Markov process      81
Homogeneous transition function      80
Hypercontractivity      206
Image of a Markov process      87
Increasing process      119
Independent, increments      96
Index of a Bessel process      440
Index of a stable law      115
Indistinguishable      19
Infinitely divisible      115
Infinitesimal generator      281
Initial distribution      81
Innovation process      175
Instantaneously reflecting      307
Integrable additive functional      410
Integral, stochastic integral      138 140 141
Integration by parts formula      146
Invariant $\sigma$ -field      423
Invariant events      423
Invariant function      423
Invariant measure      409
Irregular points      98
Iterated logarithm, law of the      56
Ito formula      147
Ito integral      138
Ito measure      482
Ito measure of excursions      482
Ito processes      298
Ito — Tanaka formula      223
Joint law of ( $\tilde{T}_{a}$ , $L_{\tilde{T}_{a}}$ )      265
Kailath — Segal identity      159
Kazamaki's criterion      331
Kazamaki's criterion is not a necessary condition      384
Kernel      79
Killed      100
Killed Brownian motion      87
Knight's identity      504
Knight's theorem      183
Kolmogorov Extension Theorem      34
Kolmogorov's continuity criterion      19
Kunita — Watanabe inequality      127
L log L class      58
Lamperti's relation      452
Langevin's equation      378
Large deviations of Brownian motion      345
Last exit times      408
Law of a process      34
Law of large numbers for local martingales      186
Lebesgue theorem for stochastic integrals      142
Levy characterization theorem      150 158
Levy measure      115
Levy process      96
Levy — Khintchine formula      115
Limit-quotient theorem      427
Linear continuous Markov processes      300
Linear stochastic equation      377
Local extrema of BM      113
Local martingales      123
Local time of a continuous semimartingale      222
Local time of Brownian motion      238
localization      123
Locally bounded process      140
Markov process      81
Markov processes, linear      300
Markov property      83 94
Markov property of BM, strong      102 156
Markov property, strong      202
Markovian      84
Martingale      51
Martingale problem      296
Master formula      475
Maximal inequality      53
Maximum principle, positive      283
Meander, Brownian meander      493
Measurable process      126
Measure, associated with an additive functional      410
Minkowski inequality for local martingales      136
Modification      19
Modulus of continuity, Levy's      30
Monotone class theorem      2
Motion, killed brownian      87
Motion, reflected brownian      86 238
Motion, skew brownian      87 292
Motion, standard linear brownian      19
Natural boundary      305
Natural filtration      42
Newtonian potential      100
Newtonian potential kernel      100
Normalized excursion      486
Normalized excursions      486
Novikov's criterion      332
Occupation time      20 401
Occupation times formula      224
Operateur carre du champ      351
Optional $\sigma$ -field      172
Optional process      172
Optional projection      173
Optional stopping      69
Optional stopping theorem      69
Ornstein — Uhlenbeck process      37
Orthogonal martingales      145
Papanicolaou — Stroock — Varadhan theorem      526
Parameter of a OU process      37
Parameter of a Poisson process      58 471
Path decomposition      255 318
Pathwise uniqueness      367
Pitman's Theorem      253
Point process      471
Points of increase of Brownian motion      461
Poisson ( $\mathcal{F}_{t}$ )-point process      474
Poisson point process      474
Poisson process      471
Polar functions for BM      24
Polar functions for the $BM^{2}$ : they include the functions of bounded variation      197
Polar sets      191

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