Stochastic Analysis for Gaussian Random Processes and Fields : With Applications

Vidyadhar S. Mandrekar

ISBN 10: 1498707815 / ISBN 13: 9781498707817

Editore: Chapman And Hall/CRC, 2015

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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 fractional Brownian motion, and equivalence and singularity of Gaussian random fields. The book also describes applications in finance and spatial statistics and presents results on Dirichlet forms and associated Markov processes.

Codice articolo 9781498707817

Dati bibliografici

• Titolo: Stochastic Analysis for Gaussian Random Processes and Fields : With Applications
• Editore: Chapman And Hall/CRC
• Data di pubblicazione: 2015
• Lingua: Inglese
• ISBN 10: 1498707815
• ISBN 13: 9781498707817
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 240 L x 161 A x 16 P (millimetri) 240 millimetri di larghezza per 161 millimetri di altezza per 16 millimetri di profondità
• Peso: 473 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.