Ukrainian Mathematical Bulletin

Volume 4, Issue 1, 2007 pp. 57-78.

Stochastic Equations with Local Time and Generalized Diffusion Processes

Authors: Sergey Ya. Makhno
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine, 74 Rosa Luxemburg Str., 83114, Donetsk, Ukraine, makhno@iamm.ac.donetsk.ua

Summary: We consider solutions of stochastic equations that contain local time for the unknown process, and prove that solutions of these equations are generalized diffusion processes in the sense of Portenko. We study the generalized diffusion coefficients, obtain a probability representation of the solution of the conjugation problem for linear second order parabolic equations in the form of functionals of solutions of a stochastic equation with local time.

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