Stochastic Analysis for Gaussian Random Processes and Fields: With Applications

ISBN-13: 9780367738143 / Angielski / Miękka / 2020 / 201 str.

Vidyadhar S. Mandrekar; Leszek Gawarecki

Opis

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

Spis treści

Covariances and Associated Reproducing Kernel Hilbert Spaces. Gaussian Random Fields. Stochastic Integration for Gaussian Random Fields. Skorokhod and Malliavin Derivatives for Gaussian Random Fields. Filtering with General Gaussian Noise. Equivalence and Singularity. Markov Property of Gaussian Fields. Markov Property of Gaussian Fields and Dirichlet Forms. Bibliography. Index.

O autorze

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.