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Stochastic Analysis for Gaussian Random Processes and Fields: With Applications

Stochastic Analysis for Gaussian Random Processes and Fields: With Applications

Stochastic Analysis for Gaussian Random Processes and Fields: With Applications
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Stochastic Analysis for Gaussian Random Processes and Fields: With Applications Hardback - 2015

by MANDREKAR, VIDYADHAR S.; GAWARECKI, LESZEK

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  • Title Stochastic Analysis for Gaussian Random Processes and Fields: With Applications
  • Author MANDREKAR, VIDYADHAR S.; GAWARECKI, LESZEK
  • Binding Hardback
  • Edition INDIAN EDITIONS
  • Condition New
  • Pages 202
  • Volumes 1
  • Language ENG
  • Publisher CRC Press
  • Publication date 2015-06-23
  • Features Bibliography, Index
  • Bookseller's Inventory # 23901269
  • ISBN 9781498707817 / 1498707815
  • Weight 1.5 lbs (0.68 kg)
  • Dimensions 9.2 x 6.2 x 0.6 in (23.37 x 15.75 x 1.52 cm)
  • Category Mathematics
  • Library of Congress subjects Stochastic processes, Gaussian processes
  • Library of Congress Catalogue Number 2015007941
  • Dewey Decimal Code 519.24
  • Quantity available 5

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From the publisher

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 It 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.

About the author

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.

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