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Aspects of Brownian Motion
丛书 Universitext
学科 Mathematics and Probability Theory and Stochastic Processes
出版社 Springer Berlin Heidelberg
DOI 10.1007/978-3-540-49966-4
版权 2008
ISBN 978-3-540-22347-4 (Print) 978-3-540-49966-4 (Online)
学科分类 数学和统计学
学科 Mathematics and Probability Theory and Stochastic Processes
Roger Mansuy
Marc Yor
主要内容：
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-Watson distribution, Brownian lace.
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, principal values, Yamada’s formulae, Dirichlet
processes, Bertoin’s excursion theory for BES(d).
Chapter 11: Riemann Zeta function, Jacobi theta function, Convolution
of Hitting times, Chung’s identity.
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