Positivity of transition probabilities of infinite-dimensional diffusion processes on ellipsoids

Oxana Manita

Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119991, Russia

Abstract: We consider diffusion processes in Hilbert spaces with constant non-degenerate diffusion operators and show that, under broad assumptions on the drift, the transition probabilities of the process are positive on ellipsoids associated with the diffusion operator. This is an infinite-dimensional analogue of positivity of densities of transition probabilities. Our results apply to diffusions corresponding to stochastic partial differential equations.

Keywords: Diffusion process in Hilbert space; SPDE; support of distribution; positive density; mild solution; variational solution; Kolmogorov equation.

MSC: 60G07, 35K90, 35K15, 35B09

Language: English

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