On the Zakai Equation of Filtering with Gaussian Noise

  • L. Gawarecki
  • V. Mandrekar
Part of the Trends in Mathematics book series (TM)


The purpose of this work is to present an analogue of the Zakai type equation in case the noise is a Gaussian process, including fractional Brownian motion (fBm). The problem is of interest in view of the fact that the signal sent through the internet is contaminated by the noise given by fBm ([6]). Recently, a similar filtering problem with fBm noise was considered in [1]. However, the authors considered a non—Markovian signal process. The assumption of the Markov property on the signal is realistic. This also leads to a recursive equation, which is easily tractable, and is widely studied ([11, 5]).


Brownian Motion Fractional Brownian Motion Reproduce Kernel Hilbert Space Stochastic Partial Differential Equation Martingale Problem 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • L. Gawarecki
    • 1
  • V. Mandrekar
    • 2
  1. 1.Department of Science and Mathematics Kettering UniversityUSA
  2. 2.Department of Statistics and Probability Michigan State University Wells HallUSA

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