Naslov
Potential theory of subordinate killed Brownian motion

Autori
Kim, Panki ; Song, Renming ; Vondraček, Zoran

Izvornik
Transactions of the American Mathematical Society (0002-9947) 371 (2019), 6; 3917-3969

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

Ključne riječi
subordinate killed Brownian motion, subordinate Brownian motion, harmonic functions, Harnack inequality, boundary Harnack principle

Sažetak
Let $W^D$ be a killed Brownian motion in a domain $D\subset \R^d$ and $S$ an independent subordinator with Laplace exponent $\phi$. The process $Y^D$ defined by $Y^D_t=W^D_{; ; ; ; ; ; S_t}; ; ; ; ; ; $ is called a subordinate killed Brownian motion. It is a Hunt process with infinitesimal generator $-\phi(-\Delta|_D)$, where $\Delta|_D$ is the Dirichlet Laplacian. In this paper we study the potential theory of $Y^D$ under a weak scaling condition on the derivative of $\phi$. We first show that non-negative harmonic functions of $Y^D$ satisfy the scale invariant Harnack inequality. Subsequently we prove two types of scale invariant boundary Harnack principles with explicit decay rates for non-negative harmonic functions of $Y^D$. The first boundary Harnack principle deals with a $C^{; ; ; ; ; ; 1, 1}; ; ; ; ; ; $ domain $D$ and non-negative functions which are harmonic near the boundary of $D$, while the second one is for a more general domain $D$ and non-negative functions which are harmonic near the boundary of an interior open subset of $D$. The obtained decay rates are not the same, reflecting different boundary and interior behaviors of $Y^D$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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