Some aspects of Brownian motion: 2 Some recent martingale problems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel, [u.a.]
Birkhäuser
[1997]
|
| Series: | Lectures in mathematics
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 144 Seiten Illustrationen |
| ISBN: | 3764357177 0817657177 |
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MARC
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| 245 | 1 | 0 | |a Some aspects of Brownian motion |n 2 |p Some recent martingale problems |c Marc Yor |
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Table of Contents
10 On principal values of Brownian and Bessel local times 1
10.1 Yamada's formulae 2
10.2 A construction of stable processes 4
10.3 Distributions of principal values of Brownian local times, taken
at an independent exponential time 5
10.4 Bertoin's excursion theory for BES(d), 0 d 1 6
Comments on Chapter 10 9
11 Probabilistic representations of the Riemann zeta function 11
11.1 The Riemann zeta function and the 3 diineiisional Bessel process 11
11.2 The agreement formulae 14
11.3 A discussion of the identity (11.8) 16
11.4 A strengthening of Knight's identity 19
11.5 Another probabilistic representation of the Riemaim zeta function 22
11.6 Some generalizations related to Bessel processes 22
11.7 Some relations between X" and E""1 = av_x + a'v_, 26
11.8 C(s) as a function otv 29
Comments on Chapter 11 31
12 Some examples and applications of enlargements of filtrations 32
12.1 Initial enlargements 33
12.2 Progressive enlargements 41
12.3 Applications to some path decompositions 13
Comments on Chapter 12 49
13 Martingale inequalities at any time 51
13.1 A global extension of the BG inequalities 51
13.2 An application to Brownian motion with dimension ;/
increasing to infinity 55
13.3 A finer extension of the BG inequalities 56
13.4 The role of BMO in some inequalities 58
Comments on Chapter 13 60
XII Table of Contents
14 On the martingales which vanish on the set of Brownian zeroes — 61
14.1 Preliminaries and some applications of the balayage formula 62
14.2 A characterization of the elements of M\ 66
14.3 The resolution of some conditional equations 73
14.4 Some Brownian martingales with a given local time,
or supremum process 76
Comments on Chapter 14 78
15 On Azema's martingales and the chaos representation property — 79
15.1 On Azema's first and second martingales 79
15.2 Azema's first martingale enjoys the chaos representation property 81
15.3 Some partial results about Azema's second martingale 85
15.4 On Emery's martingales 87
Comments on Chapter 15 93
16 The filtration of truncated Brownian motion 94
16.1 The structure of (:Ft~ = £°: t 0) martingales 94
16.2 Some Markov Processes with respect to (££,; a 0) 99
16.3 Some results on (££,; o£E) martingales 101
Comments on Chapter 16 102
17 The Brownian filtration, Tsirel'son's examples, and
Walsh's Brownian motions 103
17.1 On probability measures locally equivalent to Wiener measure 104
17.2 Walsh's Brownian motions and spider martingales 107
17.3 Some examples of loss of information for Brownian motion 114
Comments on Chapter 17 122
Epilogue to Chapter 17 123
18 Complements relative to Part I (Chapters 1 to 9) 124
18.0 Some misprints 124
18.1 On Chapter 1 125
18.2 On Chapter 2 126
18.3 On Chapter 3 127
18.4 On Chapter 6 128
18.5 On Chapters 8 and 9 129
18.6 Browiiian motion and hyperbolic functions 132
Bibliography 135
Index 142 |
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| author | Yor, Marc 1949-2014 |
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| bvnumber | BV011396215 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011396215 |
| illustrated | Illustrated |
| indexdate | 2025-03-26T17:00:40Z |
| institution | BVB |
| isbn | 3764357177 0817657177 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007660939 |
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| physical | XII, 144 Seiten Illustrationen |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Lectures in mathematics |
| spelling | Yor, Marc 1949-2014 (DE-588)120628635 aut Some aspects of Brownian motion 2 Some recent martingale problems Marc Yor Basel, [u.a.] Birkhäuser [1997] XII, 144 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics (DE-604)BV007924235 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007660939&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yor, Marc 1949-2014 Some aspects of Brownian motion |
| title | Some aspects of Brownian motion |
| title_auth | Some aspects of Brownian motion |
| title_exact_search | Some aspects of Brownian motion |
| title_full | Some aspects of Brownian motion 2 Some recent martingale problems Marc Yor |
| title_fullStr | Some aspects of Brownian motion 2 Some recent martingale problems Marc Yor |
| title_full_unstemmed | Some aspects of Brownian motion 2 Some recent martingale problems Marc Yor |
| title_short | Some aspects of Brownian motion |
| title_sort | some aspects of brownian motion some recent martingale problems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007660939&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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