Numerical method for solving stochastic differential equations with Poissonian white shot noise

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We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if the Poissonian noise approaches the Gaussian white noise. The accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by Poissonian white shot noise in a spatially periodic potential. We find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the Poissonian white shot noise; this holds true even if the limit of Gaussian white noise is approached.
Publisher
AMER PHYSICAL SOC
Issue Date
2007-07
Language
English
Article Type
Article
Keywords

NON-MARKOVIAN PROCESSES; FLUCTUATING PARAMETERS; MASTER-EQUATIONS; INDUCED TRANSPORT; BROWNIAN MOTORS; DRIVEN; DIFFUSION; SYSTEMS; STATISTICS; DYNAMICS

Citation

PHYSICAL REVIEW E, v.76, no.1, pp.3948 - 3955

ISSN
1539-3755
DOI
10.1103/PhysRevE.76.011109
URI
http://hdl.handle.net/10203/89743
Appears in Collection
CH-Journal Papers(저널논문)
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