Trace estimates for stable processes

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 involve...

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Bibliographic Details
Published in:Probability theory and related fields 2008-11, Vol.142 (3-4), p.313-338
Main Authors: Bañuelos, Rodrigo, Kulczycki, Tadeusz
Format: Article
Language:English
Subjects:
Brownian motion
Domains
Economics
Eigenvalues
Estimates
Euclidean space
Exact sciences and technology
Finance
Fourier transforms
General topics
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Partitions (mathematics)
Probability
Probability and statistics
Probability Theory and Stochastic Processes
Quantitative Finance
Sciences and techniques of general use
Smoothness
Statistics for Business
Stochastic processes
Studies
Theoretical
Theory
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Summary: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.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-007-0106-x