On the lifetime of a conditioned brownian motion:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Dr. Hut
2012
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 132 S. graph. Darst. 210 mm x 148 mm, 230 g |
| ISBN: | 9783843902977 3843902976 |
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| 245 | 1 | 0 | |a On the lifetime of a conditioned brownian motion |c Matthias Erven |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a München |b Dr. Hut |c 2012 | |
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Datensatz im Suchindex
| _version_ | 1804148870335168512 |
|---|---|
| adam_text | Titel: On the lifetime of a conditioned Brownian motion
Autor: Erven, Matthias
Jahr: 2012
Contents
1. Introduction 1
1. On the lifetime of a conditioned Brownian motion
on a domain divided into two subdomains by a path
with small gaps 7
2. The setting 9
2.1. The domain........................... 9
2.2. The results........................... 9
3. Preliminaries 13
3.1. Definitions of boundary smoothness ............. 13
3.2. Riemann mapping theorem and conformal maps ...... 15
3.3. Properties of Green functions and Poisson kernels...... 23
3.3.1. Definition........................ 23
3.3.2. Existence of the Green function in our setting .... 25
3.3.3. Existence of the Poisson kernel............ 31
3.3.4. Basic properties of Green functions.......... 32
3.3.5. Green function, Poisson kernel and conformal map-
pings ........................... 32
3.3.6. Green function and Poisson kernel estimates..... 33
3.3.7. Estimates on higher order Green function derivatives 37
3.3.8. Green function estimates - further estimates on the
logarithm........................ 38
3.4. Some facts on Brownian motion................ 40
3.4.1. Brownian motion.................... 40
3.4.2. Conditioned Brownian motion ............ 42
3.4.3. Continuity of E y/x (tn).................. 44
3.5. Further related results concerning conditioned Brownian mo-
tion ............................... 47
3.5.1. Connection to elliptic systems and the positivity pre-
serving property.................... 47
3.5.2. Maximal lifetime and a conjecture.......... 48
3.5.3. Maximal lifetime and domain shape......... 50
4. Convergence of E y/x (tn) 53
4.1. Convergence of E y/x (tn) ...................... 53
4.2. Convergence of E y/x (tn)- both points in A ......... 58
4.3. Convergence of E y/x (tn) - one point in A, one in B..... 63
5. Moving x and y away from the gaps 87
II. An example for a multiply connected domain where
maximal lifetime of conditioned Brownian motion oc-
curs for a pair of interior points 93
6. A multiply connected domain 95
6.1. The domain........................... 95
6.2. Lifetimes for small gap widths................. 98
6.3. Computation of some explicit values............. 105
7. Maximal lifetime for interior points 113
Appendices 119
A. Convergence of Ehe/x (tn Bc(y)) 119
B. Sub- and supersolution of a special Dirichlet problem 125
|
| any_adam_object | 1 |
| author | Erven, Matthias |
| author_facet | Erven, Matthias |
| author_role | aut |
| author_sort | Erven, Matthias |
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| building | Verbundindex |
| bvnumber | BV039913229 |
| ctrlnum | (OCoLC)780132725 (DE-599)DNB1019448407 |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| id | DE-604.BV039913229 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:14:00Z |
| institution | BVB |
| isbn | 9783843902977 3843902976 |
| language | English |
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| physical | VIII, 132 S. graph. Darst. 210 mm x 148 mm, 230 g |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Dr. Hut |
| record_format | marc |
| series2 | Mathematik |
| spelling | Erven, Matthias Verfasser aut On the lifetime of a conditioned brownian motion Matthias Erven 1. Aufl. München Dr. Hut 2012 VIII, 132 S. graph. Darst. 210 mm x 148 mm, 230 g txt rdacontent n rdamedia nc rdacarrier Mathematik Zugl.: Köln, Univ., Diss., 2011 (DE-588)4113937-9 Hochschulschrift gnd-content HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024771854&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Erven, Matthias On the lifetime of a conditioned brownian motion |
| subject_GND | (DE-588)4113937-9 |
| title | On the lifetime of a conditioned brownian motion |
| title_auth | On the lifetime of a conditioned brownian motion |
| title_exact_search | On the lifetime of a conditioned brownian motion |
| title_full | On the lifetime of a conditioned brownian motion Matthias Erven |
| title_fullStr | On the lifetime of a conditioned brownian motion Matthias Erven |
| title_full_unstemmed | On the lifetime of a conditioned brownian motion Matthias Erven |
| title_short | On the lifetime of a conditioned brownian motion |
| title_sort | on the lifetime of a conditioned brownian motion |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024771854&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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