The Annals of Applied Probability

Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems

P. Del Moral

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Abstract

In the paper we study interacting particle approximations of discrete time and measure-valued dynamical systems. These 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 systems 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.

Article information

Source
Ann. Appl. Probab., Volume 8, Number 2 (1998), 438-495.

Dates
First available in Project Euclid: 9 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1028903535

Digital Object Identifier
doi:10.1214/aoap/1028903535

Mathematical Reviews number (MathSciNet)
MR1624949

Zentralblatt MATH identifier
0937.60038

Subjects
Primary: 60G57: Random measures 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 93E11: Filtering [See also 60G35]

Keywords
Nonlinear filtering measure-valued processes interacting and branching particle systems genetic algorithms

Citation

Del Moral, P. Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems. Ann. Appl. Probab. 8 (1998), no. 2, 438--495. doi:10.1214/aoap/1028903535. https://projecteuclid.org/euclid.aoap/1028903535


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