ENGLISH

Multidimensional Stochastic Processes as Rough Paths: Theory and Applications

By Peter K. Friz , Nicolas B. Victoir

Book information

Publisher
Cambridge University Press
Year
2010
ISBN
0521876079, 9780521876070, 9780511680045
LCC
QA274.23 .F746 2010
Language
english
Format
PDF
Filesize
4 MB (3796411 bytes)
Series
Cambridge Studies in Advanced Mathematics 120
Edition
1
Pages
672\672
Scanned
yes
Time added
2010-05-31 15:29:46

Description

Rough path analysis provides a fresh perspective on Ito's 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 successful 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.

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