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Boundary behavior of harmonic functions for subordinate Brownian motion
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 김판기 | - |
dc.contributor.author | 이윤주 | - |
dc.date.accessioned | 2017-07-14T00:39:58Z | - |
dc.date.available | 2017-07-14T00:39:58Z | - |
dc.date.issued | 2013-02 | - |
dc.identifier.other | 000000008789 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121260 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 김판기. | - |
dc.description.abstract | In this thesis, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion $X$ is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion $X$ in a bounded $\kappa$-fat open set | - |
dc.description.abstract | if $u$ is a positive harmonic function with respect to $X$ in a bounded $\kappa$-fat open set $D$ and $h$ is a positive harmonic function in $D$ vanishing on $D^c$, then the non-tangential limit of $u/h$ exists almost everywhere with respect to the Martin-representing measure of $h$. Under the gaugeability assumption, relative Fatou theorem is true for operators obtained from the generator of pure-jump subordinate Brownian motion in bounded $\kappa$-fat open set $D$ through non-local Feynman-Kac transforms. | - |
dc.description.tableofcontents | 1. Introduction
2. Preliminaries 2.1. Subordinate Brownian motion 2.2. Our hypothesis (A1) and its basic consequences 3. Oscillation of harmonic functions 3.1. Estimates on Levy density 3.2. Oscillation 4. Relative Fatou theorem 4.1. Hypothesis (A2) and its consequences 4.2. Martin kernel 4.3. Proof of the relative Fatou theorem 5. Relative Fatou theorem under non-local Feynman-Kac transforms 5.1. Non-local Feynman-Kac transforms 5.2. Stability of the relative Fatou theorem | - |
dc.format | application/pdf | - |
dc.format.extent | 1282006 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | subordinate Brownian motion | - |
dc.subject | relative Fatou type theorem | - |
dc.subject | Martin kernel | - |
dc.subject | Martin boundary | - |
dc.subject | harmonic function | - |
dc.subject | Martin representation | - |
dc.subject.ddc | 510 | - |
dc.title | Boundary behavior of harmonic functions for subordinate Brownian motion | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Yunju Lee | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 59 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2013-02 | - |
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