Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems

Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems (1996)

Cached

Download Links

[www-sv.cict.fr]

by P. Del Moral

Venue:	Ann. Appl. Prob
Citations:	16 - 6 self

BibTeX

@ARTICLE{Moral96measurevalued,
    author = {P. Del Moral},
    title = {Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems},
    journal = {Ann. Appl. Prob},
    year = {1996},
    volume = {8},
    pages = {438--495}
}

Bookmark

OpenURL

Abstract

In the paper we study interacting particle approximations of discrete time and measure valued dynamical systems. Such systems have arisen in such diverse scientific disciplines as physics and signal processing. We give conditions for the so-called particle density profiles to converge to the desired distribution when the number of particles is growing. The strength of our approach is that is applicable to a large class of measure valued dynamical system arising in engineering and particularly in nonlinear filtering problems. Our second objective is to use these results to solve numerically the nonlinear filtering equation. Examples arising in fluid mechanics are also given. 1 Introduction 1.1 Measure valued processes Let (E; fi(E)) be a locally compact and separable metric space, endowed with a Borel oe-field, state space. Denote by P(E) be the space of all probability measures on E with the weak topology. The aim of this work is the design of a stochastic particle system approach fo...

Citations

2289	Adaptation in Natural and Artificial Systems - Holland - 1975
2262	Convergence of Probability Measures - Billingsley - 1968
1128	Probability inequalities for sums of bounded random variables - Hoeffding - 1963
750	Novel approach to nonlinear/non-Gaussian Bayesian state estimation - Gordon, Salmond, et al. - 1993
514	Stochastic processes and filtering theory - Jazwinski - 1970
183	Probability Measures on Metric Spaces - Parthasarathy - 1967
47	Prescribing a system of random variables by conditional distributions, Theor - Dobrushin - 1970
35	Asymptotic behavior of the nonlinear filtering errors of Markov processes - Kunita - 1971
25	Filtrage non linéaire et équations aux derivées partielles stochastiques associées. École d’été de Probabilités de Saint-Flour - Pardoux - 1989
24	Exact finite-dimensional filters for certain diffusions with nonlinear drift - Bene˘s - 1981
20	Convergence of a branching particle method to the solution of the Zakai equation - Crisan, Gaines, et al. - 1998
19	A particle approximation of the solution of the Kushner-Stratonovitch equation. Probab. Theory Related Fields - Crisan, Lyons - 1999
16	A limit theorem of branching processes and continuous state branching processes - Watanabe - 1968
13	Une Théorie Asymptotique des Algorithmes Génétiques - Cerf - 1994
13	Stochastic evolution equations and related measure processes - Dawson - 1975
13	Propagation of chaos for a class of non linear parabolic equations - McKean
12	The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles - Braun, Hepp - 1977
11	Nonlinear filtering and measure valued processes - Crisan, Lyons - 1997
11	Central limit theorem for a system of Markovian particles with mean field interaction - Shiga, Tanaka - 1985
10	Des resultats de non-existence de filtre de dimension finie - Chaleyat-Maurel, Michel - 1984
10	Stochastic differential equations occurring in the estimation of continuous parameter stochastic processes. Teor. Veroyatnost. i Primenen - Kallianpur, Striebel - 1969
9	Topics in nonlinear filtering theory - Ocone - 1980
8	Moral, “Non-linear filtering: Interacting particle solution - Del
8	Moral, R'esolution particulaire des probl`emes d'estimation et d'optimisation nonlin 'eaires, Th`ese de l'Universit'e Paul Sabatier, Rapport LAAS n o 94269, Juin - Del - 1994
7	Optimal nonlinear filtering in GPS/INS integration - Carvalho, Moral, et al. - 1997
7	R'esolution particulaire et traitement non-lin'eaire du signal : Application Radar/Sonar. Traitement du signal, Septembre - P, NOYER, et al. - 1995
6	Markov processes with a large number of locally interacting components: Existence of a limit process and its ergodicity - DOBRUSHIN - 1971
5	A propagation of chaos result for a system of particles with moderate interaction. Stochastic Process - Méléard, Roelly-Coppoletta - 1987
5	Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated - Sznitman - 1984
4	Filtrage optimal non lin'eaire du signal GPS NAVSTAR en racalage de centrales de navigation, Th`ese de L'Ecole Nationale Sup'erieure de l'A'eronautique et de l'Espace - CARVALHO - 1995
4	Development of a marine integrated navigation system - LIANG, McMILLAN - 1989
3	Moral, Non linear filtering using random particles Theor - Del - 1995
3	Traitement nonlin 'eaire du signal par reseau particulaire : Application Radar. quatorzi`eme colloque GRETSI, Juan les Pins - P, RIGAL, et al. - 1993
3	On the Convergence and the applications of the generalized Simulated Annealing. Publication du Laboratoire de Statistique et Probabilit'es de l'Universit'e Paul Sabatier - Moral, Miclo, et al. - 1996
3	Conditional Markov processes, Theor - Stratonovich - 1960
3	Topics in propagation of chaos. Ecole d"et'e de probabilit'es de Saint-Flour - SZNITMAN - 1989
2	Moral, Asymptotic Properties of Non-Linear Particle Filters, Publications du Laboratoire de Statistiques et Probabilit'es, Universit'e Paul Sabatier, No - Del
2	On stochastic equations in the theory of conditional Markov processe, Theor - Shiryaev - 1966
2	On Invariant Measures of Filtering - Stettner - 1989
1	The Nonlinear Filtering Problem - Crisan - 1996
1	Moral, Non-linear Filtering: Monte Carlo Particle Resolution, Publications du Laboratoire de Statistiques et Probabilit'es, Universit'e Paul Sabatier, No - Del
1	Random processes defined through the interaction of an infinite particle system - Spitzer
1	Coupling of non-linear control with a stochastic filter for state estimation : Application on a free radical polimerization reactor - Gauthier