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D. T. Gillespie, “Exact Numerical Simulation of the Ornstein-Uhlenbeck Process and Its Integral,” Physical Review E, Vol. 54, No. 2, 1996, pp. 2084-2091. http://dx.doi.org/10.1103/PhysRevE.54.2084

has been cited by the following article:

• TITLE: Simulation of Thermal Explosion of Catalytic Granule in Fluctuating Temperature Field

  AUTHORS: Igor Derevich, Daria Galdina

  KEYWORDS: Stochastic Ordinary Differential Equation; Autocorrelation Function; Heat Explosion; Semenov’s Diagram; Temperature Fluctuations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.1 No.5, September 27, 2013

  ABSTRACT: Method for numerical simulation of the temperature of granule with internal heat release in a medium with random temperature fluctuations is proposed. The method utilized the solution of a system of ordinary stochastic differential equations describing temperature fluctuations of the surrounding and granule. Autocorrelation function of temperature fluctuations has a finite decay time. The suggested method is verified by the comparison with exact analytical results. Random temperature behavior of granule with internal heat release qualitatively differs from the results obtained in the deterministic approach. Mean first passage time of granules temperature intersecting critical temperature is estimated at different regime parameters.