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Theory of Probability and Mathematical Statistics



Diffusion processes in a composite environment

S. Ya. Makhno

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Abstract: The sufficient conditions of weak convergence of solutions of stochastic equations in the space with barriers are obtained. The number of barriers grows to infinity and in limit they fill some segment. The equation for the limit process is given.

Keywords: stochastic equation, local time of process, limit behavior, weak convergence.

Bibliography:
1. K. Yosida. Functional Analysis,Springer - Verlag, 1965.
2. J.F. Le Gall. On one dimensional stochastic equations involving local time of unknown processes,Lecure Notes in Mathematics, v. 1095, p. 51--82, 1983.
3. S.Ya. Makhno. Stochastic Equation. Limit theorem, Naukova Dumka, Kyiv, 2012. (in Russia)
4. M.I. Portenko. Processes of Diffusion in Media with Membranes, Institute of Mathematics, Kyiv, 1995. (in Ukrainian)
5. S.B. Stechkin. Clarification of one proof in a book in.V. Glivenko “Integral of Stilt'esa”, Russian Mathematical Surveys, 1948, v.3a n. 6, pp. 213--215.