Click Here to Download: https://ouo.io/0taJ8h Stochastic Analysis for Gaussian Random Processes and Fields With Applications By: Vidyadhar S. Mandrekar Publisher: Chapman and Hall/CRC Print ISBN: 9781498707817, 1498707815 eText ISBN: 9781498707824, 1498707823 Edition: 1st Copyright year: 2015 Format: PDF Available from $ 23.18 USD SKU 9781498707824R90 Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs). The book begins with preliminary results on covariance and associated RKHS before introducing the Gaussian process and Gaussian random fields. The authors use chaos expansion to define the Skorokhod integral, which generalizes the Itô integral. They show how the Skorokhod integral is a dual operator of Skorokhod differentiation and the divergence operator of Malliavin. The authors also present Gaussian processes indexed by real numbers and obtain a Kallianpur–Striebel Bayes' formula for the filtering problem. After discussing the problem of equivalence and singularity of Gaussian random fields (including a generalization of the Girsanov theorem), the book concludes with the Markov property of Gaussian random fields indexed by measures and generalized Gaussian random fields indexed by Schwartz space. The Markov property for generalized random fields is connected to the Markov process generated by a Dirichlet form.
