TY - BOOK ID - 68328876 TI - Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion PY - 2012 SN - 9781107016149 9781139233842 113923384X 1139230859 9781139230858 1139232304 9781139232302 9781139060110 1139060112 1107016142 9781139230858 1107230381 128048571X 1139233076 9786613580696 1139229397 PB - Cambridge Cambridge University Press DB - UniCat KW - Malliavin calculus. KW - Lévy processes. KW - Brownian motion processes. KW - Mathematics KW - Probability & Statistics KW - General. KW - Lévy processes. KW - Wiener processes KW - Brownian movements KW - Fluctuations (Physics) KW - Markov processes KW - Random walks (Mathematics) KW - Calculus, Malliavin KW - Stochastic analysis KW - Levy processes. UR - https://www.unicat.be/uniCat?func=search&query=sysid:68328876 AB - Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques. ER -