Stochastic analysis for Gaussian random processes and fields : with applications / Vidyadhar S. Mandrekar and Leszek Gawarecki.
Material type:
TextSeries: Monographs on statistics and applied probability ; 145.Publication details: Boca Raton : CRC Press, ©2016.Description: xxi, 179 p. ; 24 cmISBN: - 9781498707817
- 519.23 23 M273
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 519.23 M273 (Browse shelf(Opens below)) | Available | 137132 |
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| 519.23 M254 Stochastic analysis | 519.23 M262 Invariant random fields on spaces with a group action | 519.23 M272 Large deviations for Gaussian queues | 519.23 M273 Stochastic analysis for Gaussian random processes and fields : | 519.23 M289 Random times and enlargements of filtrations in a Brownian setting | 519.23 M296 Stochastic differential equations | 519.23 M363 Stochastic and deterministic averaging processers |
Includes bibliographical references and index.
Chapter 1: Covariances and Associated Reproducing Kernel Hilbert Spaces;
Chapter 2: Gaussian Random Fields;
Chapter 3: Stochastic Integration for Gaussian Random Fields; Chapter 4: Skorokhod and Malliavin Derivatives for Gaussian Random Fields;
Chapter 5: Filtering with General Gaussian Noise;
Chapter 6: Equivalence and Singularity;
Chapter 7: Markov Property of Gaussian Fields;
Chapter 8: Markov Property of Gaussian Fields and Dirichlet Forms.
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 Ito integral. They show how the Skorokhod integral is a dual operator of Skorokhod differenti.
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