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Feynman-Kac formula, λ-Poisson kernels and λ-Green functions of half-spaces and balls in hyperbolic spaces

Tomasz Byczkowski, Jacek Małecki, Tomasz Żak (2010)

Colloquium Mathematicae

We apply the Feynman-Kac formula to compute the λ-Poisson kernels and λ-Green functions for half-spaces or balls in hyperbolic spaces. We present known results in a unified way and also provide new formulas for the λ-Poisson kernels and λ-Green functions of half-spaces in ℍⁿ and for balls in real and complex hyperbolic spaces.

Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.

Niels Jacob (1993)

Revista Matemática Iberoamericana

We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.

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