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CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS 120
Editorial Board
B. BOLLOBAS,´ W. FULTON, A. KATOK, F. KIRWAN,
P. SARNAK, B. SIMON, B. TOTARO
MULTIDIMENSIONAL STOCHASTIC PROCESSES AS
ROUGH PATHS
Rough path analysis provides a fresh perspective on Ito’sˆ important theory of
stochastic differential equations. Key theorems of modern stochastic analysis
(existence and limit theorems for stochastic flows, Freidlin–Wentzell theory, the
Stroock–Varadhan support description) can be obtained with dramatic simplifications.
Classical approximation results and their limitations (Wong–Zakai, McShane’s
counterexample) receive “obvious” rough path explanations. Evidence is building that
rough paths will play an important role in the future analysis of stochastic partial
differential equations, and the authors include some first results in this direction. They
also emphasize interactions with other parts of mathematics, including Caratheodory
geometry, Dirichlet forms and Malliavin calculus.
Based on essful courses at the graduate level, this up-to-date introduction
presents the theory of rough paths and its applications to stochastic analysis.
Examples, explanations and exercises make the book accessible to graduate students
and researchers from a variety of fields.
CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS
Editorial Board:
B. Bollobas,´ W. Fulton, A. Katok, F. Kirwan, P. Sarnak, B. Simon, B. Totaro
All the titles listed below can be obtained from good booksellers or from Cambridge University
Press. For plete series listing visit: ies/?code=CSAM
Already published
70 R. Iorio & V. Iorio Fourier analysis and partial differential equations
71 R. Blei Analysis in integer and fractional dimensions
72 F. Borceux & G. Janelidze Galois theories
73 B. Bollobas´ Random graphs (2nd Edition)
74 R. M. Dudley Real analysis and probability (2nd Edition)
75 T. Sheil-plex polynomials
76 C. Voisin Hodge theory plex alge