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Potential theory of subordinate killed Brownian motion (CROSBI ID 241518)

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Kim, Panki ; Song, Renming ; Vondraček, Zoran Potential theory of subordinate killed Brownian motion // Transactions of the American mathematical society, 371 (2019), 6; 3917-3969. doi: 10.1090/tran/7358

Podaci o odgovornosti

Kim, Panki ; Song, Renming ; Vondraček, Zoran

engleski

Potential theory of subordinate killed Brownian motion

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 $Y^D$.

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

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Podaci o izdanju

371 (6)

2019.

3917-3969

objavljeno

0002-9947

1088-6850

10.1090/tran/7358

Povezanost rada

Matematika

Poveznice
Indeksiranost