Continuous Martingales and Brownian MotionSpringer Science & Business Media, 9. mar. 2013 - 602 sider 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 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions. |
Indhold
1 | |
2 | |
15 | |
3 Canonical Processes and Gaussian Processes | 33 |
Notes and Comments | 48 |
3 Optional Stopping Theorem | 72 |
15 | 87 |
41 | 111 |
2 Existence and Uniqueness in the Case of Lipschitz Coefficients | 375 |
3 The Case of Hölder Coefficients in Dimension One | 388 |
Additive Functionals of Brownian Motion | 401 |
3 Strong Markov Property | 406 |
3 Ergodic Theorems for Additive Functionals | 422 |
4 Asymptotic Results for the Planar Brownian Motion | 430 |
Notes and Comments | 436 |
2 RayKnight Theorems | 454 |
3 Itôs Formula and First Applications | 146 |
4 BurkholderDavisGundy Inequalities | 160 |
Notes and Comments | 176 |
2 Conformal Martingales and Planar Brownian Motion | 189 |
55885 | 201 |
4 Integral Representations | 209 |
Markov Processes | 220 |
2 The Local Time of Brownian Motion | 239 |
4 First Order Calculus | 260 |
Notes and Comments | 277 |
2 Diffusions and Itô Processes | 294 |
2 Feller Processes | 313 |
2 Application of Girsanovs Theorem to the Study of Wieners Space | 349 |
Notes and Comments | 362 |
3 Bessel Bridges | 463 |
Notes and Comments | 469 |
2 The Excursion Process of Brownian Motion | 480 |
3 Excursions Straddling a Given Time | 488 |
Notes and Comments | 511 |
2 Asymptotic Behavior of Additive Functionals of Brownian Motion | 522 |
3 Asymptotic Properties of Planar Brownian Motion | 531 |
Notes and Comments | 541 |
4 Hausdorff Measures and Dimension | 547 |
563 | |
581 | |
119 | 595 |
Catalogue | 605 |
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Almindelige termer og sætninger
B₁ BES³ Brownian Bridge Brownian motion cadlag Chap compute constant cont continuous local martingale continuous semimartingale converges Corollary countable defined Definition denote density equal equation equivalent Exercise exists Feller process finite variation function f Gaussian Girsanov's Girsanov's theorem hence Hint independent inequality inf{t Itô's formula Lebesgue measure Lemma Lévy processes Lévy's locally bounded M₁ Markov process Markov property mart Moreover notation o-field P₁ paths positive Borel function predictable process probability measure probability space Proposition prove random variables reader real number Remark resp respect result right-continuous Sect semi-group semimartingale sequence solution standard linear BM stochastic integral stopping strong Markov property subset T₁ Tanaka's formula Theorem time-change uniformly integrable unique vanishing X₁ Y₁ zero