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Könyv Stochastic Analysis for Gaussian Random Processes and Fields Vidyadhar S. Mandrekar

Stochastic Analysis for Gaussian Random Processes and Fields

With Applications

Szerző: Vidyadhar S. Mandrekar, Leszek Gawarecki
Nyelv: Angol
Kötés: Puha kötésű
Kiadó: Taylor & Francis Ltd
Elérhetőség: 50 % esély
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25 678 Ft
Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert spa...

Információk a könyvről

Szerző
Vidyadhar S. Mandrekar, Leszek Gawarecki
Nyelv
Angol
Kötés
Könyv - Puha kötésű
Kiadva
2020
oldal
201
EAN
9780367738143
ISBN
0367738147
Enbook ID
33479251
Kiadó
Taylor & Francis Ltd
Súly
380
Méretek
156 x 234

Teljes leírás

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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