Potential Theory of Generalized Hyperbolic Processes

Let Yt be a rotationally invariant generalized hyperbolic process in Rd , d ≥ 3. Yt can be obtained by subordinating Brownian motion with a generalized inverse Gaussian subordinator Tt. We introduce generalized inverse Gaussian and generalized hyperbolic processes in chapter 1. In chapter 2, we study the asymptotic behaviors of the Green function of Y t near zero and infinite, and jumping function of Yt near zero. We prove that Harnack inequality is valid for nonnegative harmonic functions of Yt. In chapter 3, we show that the rotationally invariant generalized hyperbolic processes in a bounded C1,1 open set D can be obtained from rotationally invariant Cauchy processes in D through a combination of a pure jump Girsanov transform and a Feynman-Kac transform. From this, we deduce that the Green functions for these two processes in D are comparable, and the sharp estimate of the Green function of Yt in D is given. In the last chapter, we show boundary Harnack principle holds true for rotationally invariant generalized hyperbolic processes.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Wang, Yun

Contributors dc:contributor

• Song, Renming

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3199168

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86854