Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations |
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Authors: | Sandra Cerrai Philippe Clément |
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Institution: | a Dip. Matematica per le Decisioni, Università di Firenze, Via C. Lombroso 6/17, I-50134 Florence, Italy b Dept. of Applied Mathematical Analysis, Technische Universiteit Delft, Mekelweg 4, 2628 CD Delft, The Netherlands |
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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. |
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Keywords: | 35B45 60J70 35B65 35J25 |
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