Stochastic Analysis for Gaussian Random Processes and Fields

With Applications
1. Auflage 2015
ISBN: 978-1-4987-0781-7
Verlag: Chapman and Hall/CRC

Buch, Englisch, 202 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 473 g

Reihe: Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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.

Autoren/Hrsg.

Mandrekar, Vidyadhar S.

Gawarecki, Leszek

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz

Inhaltsverzeichnis

Covariances and Associated Reproducing Kernel Hilbert Spaces. Gaussian Random Fields. Stochastic Integration for Gaussian Random Fields. Skorokhod and Malliavin Derivatives for Gaussian Random Fields. Filtering with General Gaussian Noise. Equivalence and Singularity. Markov Property of Gaussian Fields. Markov Property of Gaussian Fields and Dirichlet Forms. Bibliography. Index.

Über Autor(innen)

Vidyadhar Mandrekar is a professor in the Department of Statistics and Probability at Michigan State University. He earned a PhD in statistics from Michigan State University. His research interests include stochastic partial differential equations, stationary and Markov fields, stochastic stability, and signal analysis.

Leszek Gawarecki is head of the Department of Mathematics at Kettering University. He earned a PhD in statistics from Michigan State University. His research interests include stochastic analysis and stochastic ordinary and partial differential equations.