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Filtration and Prediction Problems for Stochastic Fields

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Estimation and Control Problems for Stochastic Partial Differential Equations

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 83))

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Abstract

In this chapter we investigate different models of filtration and prediction for stochastic fields generated by some stochastic differential equations. We derive stochastic integro-differentiation equations for an optimal in the mean square sense filter. We also suggest different approaches for finding the best linear estimate for a stochastic field basing on its observations in certain domain. Besides, we investigate the duality of the filtration problem and a certain optimal control problem. This chapter is based on the results published in [3, 5, 11, 12, 17, 41–44, 46, 69].

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Authors and Affiliations

  1. Department of Mathematical Methods of Operation Research, V.M. Glushkov Institute of Cybernetics National Academy of Sciences of Ukraine, Kiev, Ukraine

    Pavel S. Knopov & Olena N. Deriyeva

Authors
  1. Pavel S. Knopov
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  2. Olena N. Deriyeva
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Knopov, P.S., Deriyeva, O.N. (2013). Filtration and Prediction Problems for Stochastic Fields. In: Estimation and Control Problems for Stochastic Partial Differential Equations. Springer Optimization and Its Applications, vol 83. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8286-4_3

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