This article is cited in 2 papers

Bounded Perturbations of Two-Dimensional Diffusion Processes with Nonlocal Conditions near the Boundary

P. L. Gurevich

Peoples Friendship University of Russia

Abstract: We study the existence of Feller semigroups arising in the theory of multidimensional diffusion processes. We study bounded perturbations of elliptic operators with boundary conditions containing an integral over the closure of the domain with respect to a nonnegative Borel measure without assuming that the measure is small. We state sufficient conditions on the measure guaranteeing that the corresponding nonlocal operator is the generator of a Feller semigroup.

Keywords: diffusion process, Feller semigroup, elliptic operator, Borel measure, Hille–Yosida theorem, nonlocal condition.

UDC: 517.9+519.217.4

Received: 26.04.2007

DOI: 10.4213/mzm3939

 English version: Mathematical Notes, 2008, 83:2, 162–179

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