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Milstein GN, Tretyakov MV. Monte Carlo methods for backward equations in nonlinear filtering. ADV APPL PROBAB 2016. [DOI: 10.1239/aap/1240319577] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We consider Monte Carlo methods for the classical nonlinear filtering problem. The first method is based on a backward pathwise filtering equation and the second method is related to a backward linear stochastic partial differential equation. We study convergence of the proposed numerical algorithms. The considered methods have such advantages as a capability in principle to solve filtering problems of large dimensionality, reliable error control, and recurrency. Their efficiency is achieved due to the numerical procedures which use effective numerical schemes and variance reduction techniques. The results obtained are supported by numerical experiments.
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Abstract
While the convergence properties of many sampling selection methods can be proven, there is one particular sampling selection method introduced in Baker (1987), closely related to ‘systematic sampling’ in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. We will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.
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Gentil I, Rémillard B. Using systematic sampling selection for Monte Carlo solutions of Feynman-Kac equations. ADV APPL PROBAB 2016. [DOI: 10.1239/aap/1214950212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
While the convergence properties of many sampling selection methods can be proven, there is one particular sampling selection method introduced in Baker (1987), closely related to ‘systematic sampling’ in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. We will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.
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Monte Carlo methods for backward equations in nonlinear filtering. ADV APPL PROBAB 2016. [DOI: 10.1017/s0001867800003141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We consider Monte Carlo methods for the classical nonlinear filtering problem. The first method is based on a backward pathwise filtering equation and the second method is related to a backward linear stochastic partial differential equation. We study convergence of the proposed numerical algorithms. The considered methods have such advantages as a capability in principle to solve filtering problems of large dimensionality, reliable error control, and recurrency. Their efficiency is achieved due to the numerical procedures which use effective numerical schemes and variance reduction techniques. The results obtained are supported by numerical experiments.
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A branching particle approximation to a filtering micromovement model of asset price. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2011. [DOI: 10.1007/s11203-011-9053-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Douc R, Moulines E. Limit theorems for weighted samples with applications to sequential Monte Carlo methods. Ann Stat 2008. [DOI: 10.1214/07-aos514] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Kouritzin MA, Sun W. Rates for branching particle approximations of continuous-discrete filters. ANN APPL PROBAB 2005. [DOI: 10.1214/105051605000000539] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Affiliation(s)
- Dan Crisan
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
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