University of Illinois Urbana-Champaign

Potential Theory for Subordinate Killed Brownian Motion in Some Unbounded Domains

Zhang, Feng

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https://hdl.handle.net/2142/86864

Description

Title
Potential Theory for Subordinate Killed Brownian Motion in Some Unbounded Domains
Author(s)
Zhang, Feng
Issue Date
2006
Doctoral Committee Chair(s)
Song, Renming
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
{1,1}$ boundaries. With the help of two-sided estimates of the densityfunction of the subordinate killed Brownian motion in each domain, we are able to identify the Martin boundary and the minimal Martin boundary, and then obtain the canonical representation of the positive harmonic functions in terms of the Martin boundary and the Martin kernel. Moreover, each positive harmonic function consists of two nonnegative harmonic functions: one is purely excessive and the other is invariant under the semigroup of the subordinate killed Brownian motion. By the two-sided estimates of the Martin kernel and the canonical representation of the positive harmonic functions, we also show that the Harnack inequality and boundary Harnack principle hold for all the positive harmonic functions of the subordinate killed Brownian motion in the unbounded domains mentioned above.
Graduation Semester
2006
Type of Resource
text
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http://hdl.handle.net/2142/86864

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