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JOURNALS // Theory of Stochastic Processes // Archive

Theory Stoch. Process., 2007 Volume 13(29), Issue 3, Pages 12–21 (Mi thsp224)

This article is cited in 1 paper

One example of a random change of time that transforms a generalized diffusion process into an ordinary one

Olga V. Aryasovaa, Mykola I. Portenkob

a Institute of Geophysics, National Academy of Sciences of Ukraine, 32, Palladina Pr., Kyiv 03680, Ukraine
b Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs'ka Str., Kyiv 01601, Ukraine

Abstract: We propose a random change of time for a class of generalized di?usion processes such that the corresponding stochastic differential equation (with generalized coe?cients) is transformed into an ordinary one (its coe?cients are some non-generalized functions). It turns out that the latter stochastic differential equation has no property of the (weak) uniqueness of a solution.

Keywords: Diffusion process, random change of time, stochastic differential equation, uniqueness of solution.

MSC: 60J60, 60J35

Language: English



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