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.
Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations / S. CERRAI; P. CLEMENT. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - STAMPA. - 128:(2004), pp. 355-389. [10.1016/j.bulsci.2004.03.004]
Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations
CERRAI, SANDRA;
2004
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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.