Numerical method for solving stochastic differential equations with dichotomous noise

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We propose a numerical method for solving stochastic differential equations with dichotomous Markov noise. The numerical scheme is formulated such that (i) the stochastic formula used follows the Stratonovich-Taylor form over the entire range of noise correlation times, including the Gaussian white noise limit; and (ii) the method is readily applicable to dynamical systems driven by arbitrary types of noise, provided there exists a way to describe the random increment of the stochastic process expressed in the Stratonovich-Taylor form. We further propose a simplified Taylor scheme that significantly reduces the computation time, while still satisfying the moment properties up to the required order. The accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions.
Publisher
AMER PHYSICAL SOC
Issue Date
2006-02
Language
English
Article Type
Article
Keywords

RANDOM TELEGRAPH SIGNAL; NON-MARKOVIAN PROCESSES; COLORED-NOISE; GAUSSIAN-NOISE; INDUCED TRANSITIONS; BISTABILITY DRIVEN; ACTIVATION RATES; 1ST-PASSAGE TIME; ALGORITHM; SYSTEMS

Citation

PHYSICAL REVIEW E, v.73, no.2, pp.163 - 176

ISSN
1539-3755
DOI
10.1103/PhysRevE.73.026101
URI
http://hdl.handle.net/10203/89761
Appears in Collection
CH-Journal Papers(저널논문)
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