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Trace estimates for stable processes

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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Author information

Correspondence to Rodrigo Bañuelos.

Additional information

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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Keywords

  • Green Function
  • Heat Kernel
  • Stable Process
  • Heat Semigroup
  • Symmetric Stable Process