Stochastic solution of nonlinear and nonhomogeneous evolution problems by a differential Kolmogorov equation

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dc.creatorKeanini, R. G.
dc.date2007-08-23
dc.date.accessioned2026-07-07T08:25:15Z
dc.date.available2026-07-07T08:25:15Z
dc.descriptionA large class of physically important nonlinear and nonhomogeneous evolution problems, characterized by advection-like and diffusion-like processes, can be usefully studied by a time-differential form of Kolmogorov's solution of the backward-time Fokker-Planck equation. The differential solution embodies an integral representation theorem by which any physical or mathematical entity satisfying a generalized nonhomogeneous advection-diffusion equation can be calculated incrementally in time. The utility of the approach for tackling nonlinear problems is illustrated via solution of the noise-free Burgers and related Kardar-Parisi-Zhang (KPZ) equations where it is shown that the differential Kolmogorov solution encompasses, and allows derivation of, the classical Cole-Hopf and KPZ transformations and solutions. A second example, illustrating application of this approach to nonhomogeneous evolution problems, derives the Feynman-Kac formula appropriate to a Schrodinger-like equation.
dc.description15 pages, 2 figures, submitted SIAM J. App. Math
dc.identifierhttps://arxiv.org/abs/0708.3202
dc.identifierhttp://arxiv.org/abs/0708.3202
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136597
dc.subjectData Analysis, Statistics and Probability
dc.subjectFluid Dynamics
dc.titleStochastic solution of nonlinear and nonhomogeneous evolution problems by a differential Kolmogorov equation
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