The Malliavin Calculus and Related Topics
Publication year: 2006
ISBN: 978-3-540-28329-4
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In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s,p wards (white noise case). The Sobolev spaces D , with s is an arbitrary real number, are introduced following Watanabe’s work. Chapter 2, includes a general estimate for the density of a one-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe’s ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented.
Subject: Mathematics and Statistics, Anticipating stochastic calculus, Brownian motion, Gaussian processes, Girsanov theorem, Malliavin Calculus, Markov processes, Markov property, Skorohod integral, Stochastic differential equations, Stochastic partial differential equations, fractional Brownian motion
