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On the optimal filtering of diffusion processes

  • Moshe Zakai
Article

Summary

Let x(t) be a diffusion process satisfying a stochastic differential equation and let the observed process y(t) be related to x(t) by dy(t) = g(x(t)) + dw(t) where w(t) is a Brownian motion. The problem considered is that of finding the conditional probability of x(t) conditioned on the observed path y(s), 0≦st. Results on the Radon-Nikodym derivative of measures induced by diffusions processes are applied to derive equations which determine the required conditional probabilities.

Keywords

Differential Equation Stochastic Process Brownian Motion Probability Theory Diffusion Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Moshe Zakai
    • 1
  1. 1.Department of Electrical EngineeringTechnion - Israel Institute of TechnologyHaifaIsrael

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