Second-order algorithm for simulating stochastic differential equations with white noises

Abstract The second-order algorithm for simulating stochastic differential equations with Gaussian white noises is presented. These stochastic differential equations are universal type, among, these Gaussian white noises come from different sources. Specifically, the proposed algorithm extends previous first-order algorithm for stochastic differential equations with different white noises and second-order algorithm for stochastic differential equations with same white noise. In practice, it is proved that this algorithm is scientific.

[1]  Peter Hänggi,et al.  Numerical method for solving stochastic differential equations with Poissonian white shot noise. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  J. M. Sancho,et al.  Analytical and numerical studies of multiplicative noise , 1982 .

[3]  Mannella,et al.  Fast and precise algorithm for computer simulation of stochastic differential equations. , 1989, Physical review. A, General physics.

[4]  Matjaž Perc,et al.  Evolutionary and dynamical coherence resonances in the pair approximated prisoner's dilemma game , 2006 .

[5]  Zakieh Avazzadeh,et al.  Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion , 2018, Commun. Nonlinear Sci. Numer. Simul..

[6]  M. Perc.  Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Honeycutt.  Stochastic Runge-Kutta algorithms. II. Colored noise. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[8]  Rukiye Uzun,et al.  Noise-delayed decay in the response of a scale-free neuronal network , 2013 .

[9]  M. Perc.  Double resonance in cooperation induced by noise and network variation for an evolutionary prisoner's dilemma , 2006 .

[10]  Matjaž Perc,et al.  Thoughts out of noise , 2006 .

[11]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[12]  J. M. Sancho,et al.  Stochastic algorithms for discontinuous multiplicative white noise. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  R. Fox,et al.  Numerical simulations of stochastic differential equations , 1989 .

[14]  Svetlana Jankovic,et al.  Some analytic approximations for neutral stochastic functional differential equations , 2010, Appl. Math. Comput..

[15]  L. Mandel,et al.  Coherence theory of the ring laser , 1978 .

[16]  Habib,et al.  Second-order stochastic leapfrog algorithm for multiplicative noise brownian motion , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Roy,et al.  Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise. , 1988, Physical review. A, General physics.

[18]  Honeycutt,et al.  Stochastic Runge-Kutta algorithms. I. White noise. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[19]  Fox,et al.  Second-order algorithm for the numerical integration of colored-noise problems. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[20]  Sylvain Rubenthaler,et al.  Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process , 2003 .

[21]  Steffen Dereich,et al.  A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations , 2011 .

[22]  M Grigoriu.  Numerical solution of stochastic differential equations with Poisson and Lévy white noise. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M. Perc.  Coherence resonance in a spatial prisoner's dilemma game , 2006 .

[24]  H. Risken.  Distribution- and correlation-functions for a laser amplitude , 1965 .

[25]  Matjaz Perc,et al.  Effects of correlated Gaussian noise on the mean firing rate and correlations of an electrically coupled neuronal network. , 2010, Chaos.