Open Access
Translator Disclaimer
January, 1988 Unique Characterization of Conditional Distributions in Nonlinear Filtering
T. G. Kurtz, D. L. Ocone
Ann. Probab. 16(1): 80-107 (January, 1988). DOI: 10.1214/aop/1176991887


Let $(X, Y)$ solve the martingale problem for a given generator $A$. This paper studies the problem of uniquely characterizing the conditional distribution of $X(t)$ given observations $\{Y(s)\mid 0 \leq s \leq t\}$. We define a filtered martingale problem for $A$ and we show, given appropriate hypotheses on $A$, that the conditional distribution is the unique solution to the filtered martingale problem for $A$. Using these results, we then prove that the solutions to the Kushner-Stratonovich and Zakai equations for filtering Markov processes in additive white noise are unique under fairly general circumstances.


Download Citation

T. G. Kurtz. D. L. Ocone. "Unique Characterization of Conditional Distributions in Nonlinear Filtering." Ann. Probab. 16 (1) 80 - 107, January, 1988.


Published: January, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0655.60035
MathSciNet: MR920257
Digital Object Identifier: 10.1214/aop/1176991887

Primary: 60G35
Secondary: 60G44 , 60G57 , 60H15 , 62M20 , 93E11

Keywords: Conditional distributions , Kushner-Stratonovich equation , Martingale problem , Nonlinear filtering , Zakai equation

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • January, 1988
Back to Top