Uniqueness of the Solution to the Zakai and the Kushner–Stratonovich Equations

  • Alan Bain
  • Dan Crisan
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 60)


The conditional distribution of the signal π = {π t , t ≥ 0} is a solution of the Kushner–Stratonovich equation, whilst its unnormalised version ρ = {ρ t , t ≥ 0} solves the Zakai equation.


Dominate Convergence Theorem Observation Equation Correlate Noise Bibliographical Note Bounded Measurable Function 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Alan Bain
    • 1
  • Dan Crisan
    • 2
  1. 1.BNP Paribas 10 Harewood AvLondonUnited Kingdom
  2. 2.Department of MathematicsImperial College London 180 Queen’s GateLondonUnited Kingdom

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