International Journal of Stochastic Analysis · 1997 · 88 citations · 7 references
Natural SciencesElectrical EngineeringMathematicsDifferential EquationsDynamical SystemsStochastic ProcessesDiffusion ProcessesPerturbation MethodsPerturbation TheoryRandom WalksSingular Perturbation TheoryStochastic Differential EquationsAsymptotic NormalityDiffusion EquationDiffusion Equation ModelsRandom Walk Limit TheoremsRandom Walk LimitsSingular Perturbation Analysis
In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated random walks is explained in asymptotic terms.
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A stochastic model related to the telegrapher's equation
Mark Kac · Rocky Mountain Journal of Mathematics · 1974 · 633 citations · Full text
Engineering, Mathematics, Physics +12
Diffusion by Continuous Movements
H. C. Gupta · Journal of Mathematics and Physics · 1959 · 19 citations