On the optimal filtering of diffusion processes

  • Moshe Zakai

DOI: 10.1007/BF00536382

Cite this article as:
Zakai, M. Z. Wahrscheinlichkeitstheorie verw Gebiete (1969) 11: 230. doi:10.1007/BF00536382


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.

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

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