Asymptotic Ergodicity of the Process of Conditional Law in Some Problem of Non-linear Filtering

Abstract We consider a sample of a trajectory of an ergodic process m x through a stationary noisy observation process. We study the asymptotic ergodicity of the phase process.

[1]  Paul Malliavin,et al.  Stochastic Analysis , 1997, Nature.

[2]  M. Zakai.  On the optimal filtering of diffusion processes , 1969 .

[3]  H. Kunita.  Asymptotic behavior of the nonlinear filtering errors of Markov processes , 1971 .

[4]  Mark H. A. Davis.  On a multiplicative functional transformation arising in nonlinear filtering theory , 1980 .

[5]  J. Bismut,et al.  Diffusions conditionnelles. I. Hypoellipticité partielle , 1981 .

[6]  D. Stroock,et al.  Diffusions on an infinite dimensional torus , 1981 .

[7]  D. Stroock,et al.  The partial malliavin calculus and its application to non-linear filtering , 1984 .

[8]  D. Ocone.  Stochastic calculus of variations for stochastic partial differential equations , 1988 .

[9]  R. Elliott,et al.  Approximations to solutions of the zakai filtering equation , 1989 .

[10]  Mtw,et al.  Stochastic flows and stochastic differential equations , 1990 .

[11]  P. Florchinger.  Malliavin calculus with time dependent coefficients and application to nonlinear filtering , 1990 .

[12]  É. Pardoux,et al.  Filtrage Non Lineaire Et Equations Aux Derivees Partielles Stochastiques Associees , 1991 .

[13]  R. Léandre,et al.  Decroissance exponentielle du noyau de la chaleur sur la diagonale (I) , 1991 .

[14]  Comportement en temps long pour des problèmes de filtrage sans bruit de dynamique , 1995 .

[15]  Renormalized Differential Geometry on Path Space: Structural Equation, Curvature , 1996 .

[16]  R. Atar,et al.  Exponential stability for nonlinear filtering , 1997 .