Naslov
Potential theory of subordinate killed Brownian motion in a domain

Autori
Song, Renming ; Vondraček, Zoran

Izvornik
Probability theory and related fields (0178-8051) 125 (2003), 4; 578-592

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
killed Brownian motions ; stable processes ; subordination ; fractional Laplacian

Sažetak
Subordination of a killed Brownian motion in a bounded domain $D\subset \R^d$ via an $\alpha/2$-stable subordinator gives a process $Z_t$ whose infinitesimal generator is $-(-\Delta|_D)^{; ; ; \alpha/2}; ; ; $, the fractional power of the negative Dirichlet Laplacian. In this paper we study the properties of the process $Z_t$ in a Lipschitz domain $D$ by comparing the process with the rotationally invariant $\alpha$-stable process killed upon exiting $D$. We show that these processes have comparable killing measures, prove the intrinsic ultracontractivity of the semigroup of $Z_t$, and, in the case when $D$ is a bounded $C^{; ; ; 1, 1}; ; ; $ domain, obtain bounds on the Green function and the jumping kernel of $Z_t$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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