Filtration and Prediction Problems for Stochastic Fields

  • Pavel S. Knopov
  • Olena N. Deriyeva
Part of the Springer Optimization and Its Applications book series (SOIA, volume 83)


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].


Stochastic Field Filtering Problem Sense Filter Stochastic Parabolic Equations Orthogonal Stochastic Measure 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Pavel S. Knopov
    • 1
  • Olena N. Deriyeva
    • 1
  1. 1.Department of Mathematical Methods of Operation ResearchV.M. Glushkov Institute of Cybernetics National Academy of Sciences of UkraineKievUkraine

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