Trace estimates for stable processes
By Rodrigo Bañuelos, Tadeusz Kulczycki. 2007
50 citations recorded by the source corpus.
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 Rd. 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/4f64c2f428dbad8a5286aa145890e5997f217d48
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In Applied Mathematics
- Krzysztof Bogdan
- Mateusz Kwaśnicki
- M. Ryznar
- T. Grzywny
- Tadeusz Kulczycki
- Tomasz Jakubowski
- A. Stos
- J. Małecki
In Computational Theory and Mathematics
- Krzysztof Bogdan
- M. Ryznar
- T. Grzywny
- Mateusz Kwaśnicki
- Tadeusz Kulczycki
- A. Stos
- Tomasz Jakubowski
- Bartłlomiej Dyda
In Finance
- Mateusz Kwaśnicki
- Krzysztof Bogdan
- M. Ryznar
- T. Grzywny
- Tadeusz Kulczycki
- J. Małecki
- Xavier Ros-Oton
- Renming Song
Citations in the corpus
- Eigenvalues of the fractional Laplace operator in the interval (2010, background): “This is related to simplicity of eigenvalues λn, conjectured to hold for all α ∈ (0, 2), proved for α = 1 in [13], and extended to α ∈ [1, 2) in Proposition 3 in Section 6.”
- Spectral properties of the Cauchy process on half‐line and interval (2009, background): “For t > 0, we have (see, for example, [3, 33]) ∞ ∑”
- Heat kernel estimates for the fractional Laplacian with Dirichlet conditions (2009, background): “Some of our present techniques were inspired by [32], Theorem 4.2, of Kulczycki and Siudeja, [2], Proposition 2.9, of Bañuelos and Kulczycki, and [1], Section 4, of Bogdan and Bañuelos.”