On the Traces of symmetric stable processes on Lipschitz domains

Details On the Traces of symmetric stable processes on Lipschitz domains On the Traces of symmetric stable processes on Lipschitz domains

2009-03-06

arxiv.org/abs/0903.1198v1

Mathematics

Probability

Scientific paper

It is shown that the second term in the asymptotic expansion as $t\to 0$ of the trace of the semigroup of symmetric stable processes (fractional powers of the Laplacian) of order $\alpha$, for any $0<\alpha<2$, in Lipschitz domains is given by the surface area of the boundary of the domain. This brings the asymptotics for the trace of stable processes in domains of Euclidean space on par with those of Brownian motion (the Laplacian), as far as boundary smoothness is concerned.

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