We consider the question of robustness of the optimal nonlinear filter when the signal process X and the observation noise are possibly correlated. The signal X and observations Y are given by a SDE where the coefficients can depend on the entire past. Using results on pathwise solutions of...

In the nonlinear filtering model with signal and observation noise independent, we show that the filter depends continuously on the law of the signal. We do not assume that the signal process is Markov and prove the result under minimal integrability conditions. The analysis is based on...

In this article, we construct a mapping : D[0, [infinity])xD[0,[infinity])--D[0,[infinity]) such that if (Xt) is a semimartingale on a probability space ([Omega], , P) with respect to a filtration (t) and if (ft) is an r.c.l.l. (t) adapted process, then This is of significance when using...

Let \s{Xn, n [greater-or-equal, slanted] 0\s} and \s{Yn, n [greater-or-equal, slanted] 0\s} be two stochastic processes such that Yn depends on Xn in a stationary manner, i.e. P(Yn [epsilon] A\vbXn) does not depend on n. Sufficient conditions are derived for Yn to have a limiting distribution....

In this note we develop the theory of stochastic integration w.r.t. continuous local martingales using a simple time change technique. We allow progressively measurable integrands.