发帖
雷达卡
Author：Roger Mansuy and Marc Yor
Publication Year: 2008
该书介绍布朗运动的高级特性以及一些应用，内容有点难度，需要一定的数学基础。
Key words, chapter by chapter
Chapter 1: Gaussian space, first Wiener chaos, filtration of Brownian bridges, ergodic property, space-time harmonic functions.
Chapter 2: Quadratic functionals, L′evy’s area formula, Ornstein-Uhlenbeck process, Fubini-Wiener integration by parts.
Chapter 3: Ray-Knight theorems, transfer principle, additivity property, L′evy-Khintchine representation, generalized meanders, Bessel bridges.
Chapter 4: Ciesielski-Taylor (: CT) identities, Biane’s extensions.
Chapter 5: Winding number, Hartman-Watsondistribution, Brownianlace.
Chapter 6: Asian options, Confluent hypergeometric functions, beta and gamma variables.
Chapter 7: Kallianpur-Robbins ergodic theorem, Spitzer’s theorem, Gauss linking number.
Chapter 8: P. L′evy’s arc sine law, F. Petit’s extensions, Walsh’s Brownian motion, Excursion theory Master formulae, Feynman-Kac formula.
Chapter 9: Local time perturbation of Brownian motion, Bismut’s identity, Knight’s ratio formula.
Chapter 10:Hilbert transform,principalvalues,Yamada’sformulae,Dirichlet processes, Bertoin’s excursion theory for BES(d).
Chapter 11: Riemann Zeta function, Jacobi theta function, Convolution of Hitting times, Chung’s identity.
Aspects of Brownian Motion.pdf
(1.73 MB, 需要: 2 个论坛币)
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