Stochastic Analysis for Gaussian Random Processes and Fields

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A01=Leszek Gawarecki
A01=Vidyadhar S. Mandrekar
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Author_Leszek Gawarecki
Author_Vidyadhar S. Mandrekar
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basis
Bayes Formula
brownian
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Conditional Expectation
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Dirichlet Forms
Dirichlet Space
Disjoint Supports
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fractional
Gaussian Fields
Gaussian Random
Gaussian Random Field
Gaussian Space
Heath Jarrow Morton Model
hilbert
Hilbert Schmidt Operators
integration
kernel
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Malliavin Derivative
Markov Property
Maturity Specific Risk
motion
Negative Definite Function
Open Subsets
orthonormal
Orthonormal Basis
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Radon Nikodym Densities
reproducing
Reproducing Kernel Hilbert Spaces
Skorokhod Integral
Smooth Functional
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space
Stochastic Duration
Stochastic Integral
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T2 T1

Product details

  • ISBN 9780367738143
  • Weight: 380g
  • Dimensions: 156 x 234mm
  • Publication Date: 18 Dec 2020
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Paperback
  • Language: English
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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.

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.