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Trace estimates for stable processes
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  • Published: 30 October 2007

Trace estimates for stable processes

  • Rodrigo Bañuelos1 &
  • Tadeusz Kulczycki2 

Probability Theory and Related Fields volume 142, pages 313–338 (2008)Cite this article

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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

Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA

    Rodrigo Bañuelos

  2. Institute of Mathematics, Wrocław University of Technology, 50-370, Wrocław, Poland

    Tadeusz Kulczycki

Authors
  1. Rodrigo Bañuelos
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  2. Tadeusz Kulczycki
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Corresponding author

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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Cite this article

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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  • Received: 26 April 2007

  • Revised: 10 September 2007

  • Published: 30 October 2007

  • Issue Date: November 2008

  • DOI: 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
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