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Stochastic Analysis for Gaussian Random Processes and Fields
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Stochastic Analysis for Gaussian Random Processes and Fields : With Applications

by Leszek Gawarecki , Vidyadhar S. Mandrekar

Book Details

Format Paperback / Softback
Book Series Chapman & Hall/CRC Monographs on Statistics and Applied Probability
ISBN-10 0367738147
ISBN-13 9780367738143
Publisher Taylor & Francis Ltd
Imprint Chapman & Hall/CRC
Country of Manufacture GB
Country of Publication GB
Publication Date Dec 18th, 2020
Print length 201 Pages
Weight 380 grams
Product Classification: Sociology Probability & statistics
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This monograph presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, the authors study Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs). They explain how covariances are related to RKHSs and examine the Bayes’ formula, the filtering and analytic problem related to

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.

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