Abstract
In this paper we study the behaviour in time of the trace (the partition function) of the heat semigroup associated with symmetric stable processes in domains of R d. In particular, we show that for domains with the so called R-smoothness property the second terms in the asymptotic as t → 0 involves the surface area of the domain, just as in the case of Brownian motion.
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R. Bañuelos was supported in part by NSF Grant #0603701-DMS.
T. Kulczycki was supported in part by KBN Grant 1 P03A 020 28.
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Bañuelos, R., Kulczycki, T. Trace estimates for stable processes. Probab. Theory Relat. Fields 142, 313–338 (2008). https://doi.org/10.1007/s00440-007-0106-x
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DOI: https://doi.org/10.1007/s00440-007-0106-x