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 paper we formulate and prove a general principle which enables us to deduce limit theorems for a sequence of random variables on a finitely additive probability space.

A model of "satisficing" behavior in the repeated Prisoners Dilemma is studied. Each player has an aspiration at each date, and takes an action. [S]he switches from the action played in the previous period only if the achieved payoff fell below the aspiration level (with a probability that...

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.

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...

It has been shown previously by Nobel and Dembo (Stat. Probab. Lett. 17 (1993) 169) that, if a family of functions has the property that empirical means based on an i.i.d. process converge uniformly to their values as the number of samples approaches infinity, then continues to have the same...