Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations

Journal article (2004)

Authors

S Cerrai External organisation
P.P.J.E. Clement Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
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Published Date

2004

Language

Undefined/Unknown

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

In this paper we establish the well-posedness in C([0,);[0,1]d), for each starting point x [0,1]d, of the martingale problem associated with a class of degenerate elliptic operators which arise from the dynamics of populations as a generalization of the Fleming¿Viot operator. In particular, we prove that such degenerate elliptic operators are closable in the space of continuous functions on [0,1]d and their closure is the generator of a strongly continuous semigroup of contractions.

Author Keywords: Degenerate elliptic equations in nonregular domains; Generation of semigroup; Stochastic invariance; Fleming¿Viot operator; Martingale problem

35B45; 60J70; 35B65; 35J25