Naslov
Green function estimates and Harnack inequality for subordinate Brownian motions

Autori
Rao, Murali ; Song, Renming ; Vondraček, Zoran

Izvornik
Potential analysis (0926-2601) 25 (2006), 1; 1-27

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

Ključne riječi
Subordinate Brownian motion ; Green function ; Harnack inequality ; subordinator ; complete Bernstein function ; capacity

Sažetak
Let $X$ be a L\'evy process in $\R^d$, $d\ge 3$, obtained by subordinating Brownian motion using a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a L\'evy process with no continuous component. We study the asymptotic behavior of the Green function of $X$ near zero. Under the assumption that the Laplace exponent of the subordinator is a complete Bernstein function we also describe the asymptotic behavior of the Green function at infinity. With an additional assumption on the L\'evy measure of the subordinator we prove that the Harnack inequality is valid for nonnegative harmonic functions of $X$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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