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This book investigates key aspects of estimation and control theory for systems modeled by stochastic partial differential equations. The models presented describe many processes in turbulence theory, fluid mechanics, hydrology, astronomy and meteorology.

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Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations. It contains many results of interest to specialists in both the theory of random fields and optimal control theory who use modern mathematical tools for resolving specific applied problems, and presents research that has not previously been covered. More generally, this book is intended for scientists, graduate, and post-graduates specializing in probability theory and mathematical statistics.

The models presented describe many processes in turbulence theory, fluid mechanics, hydrology, astronomy, and meteorology, and are widely used in pattern recognition theory and parameter identification of stochastic systems. Therefore, this book may also be useful to applied mathematicians who use probability and statistical methods in the selection of useful signals subject to noise, hypothesis distinguishing, distributed parameter systems optimal control, and more. Material presented in this monograph can be used for education courses on the estimation and control theory of random fields.

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1. Two Parameter Martingales and Their Properties.- 2. Stochastic Differential Equations on the Plane.- 3. Filtration and Prediction Problems for Stochastic Fields.- 4. Control Problem for Diffusion-Type Random Fields.- 5. Stochastic Processes in a Hilbert Space.- References.

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From the book reviews:

"The book is focused on the study of stochastic (partial) differential equations of hyperbolic type. ... there are several topics treated in the book that may be of interest to specialists working in stochastic multiparameter SDEs and SPDEs, especially for those interested in problems of control and filtering." (Bohdan Maslowski, Mathematical Reviews, February, 2015)

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