Some aspects of Brownian motion 1 Some special functionals
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1992
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| Schriftenreihe: | Lectures in mathematics
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| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Some aspects of Brownian motion |n 1 |p Some special functionals |c Marc Yor |
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| adam_text | Table of Contents
1 The Gaussian space of Brownian motion 1
1.1 A realization of Brownian bridges 1
1.2 The filtration of Brownian bridges 2
1.3 An ergodic property 5
1.4 A relationship with space time harmonic functions 6
1.5 Brownian motion and Hardy s I? inequality 9
1.6 Fourier transform and Brownian motion 12
Comments on Chapter 1 13
2 The laws of some quadratic functionals of Brownian motion 15
2.1 Levy s area formula and some variants 16
2.2 Some identities in law and an explanation
of them via Fubini s theorem 21
2.3 The laws of squares of Bessel processes 23
Comments on Chapter 2 26
3 Squares of Bessel processes and Ray Knight theorems
for Brownian local times 27
3.1 The basic Ray Knight theorems 28
3.2 The Levy Khintchine representation of Q* 29
3.3 An extension of the Ray Knight theorems 32
3.4 The law of Brownian local times taken at an
independent exponential time 34
3.5 Squares of Bessel processes and squares of Bessel bridges 36
3.6 Generalized meanders and squares of Bessel processes 41
3.7 Generalized meanders and Bessel bridges 45
Comments on Chapter 3 48
4 An explanation and some extensions of
the Ciesielski Taylor identities 50
4.1 A pathwise explanation for 6 = 1 51
4.2 A reduction to an identity in law between two
Brownian quadratic functionals 52
4.3 Some extensions of the Ciesielski Taylor identities 53
4.4 On a computation of Foldes and Revesz 56
Comments on Chapter 4 57
5 On the winding number of planar Brownian motion 58
5.1 Preliminaries 58
5.2 Explicit computation of the winding number
of planar Brownian motion 61
Comments on Chapter 5 67
6 On some exponential functionals of Brownian motion
and the problem of Asian options 68
6.1 The integral moments of A^v) 70
6.2 A study in a general Markovian set up 73
6.3 The case of Levy processes 75
6.4 Application to Brownian motion 76
6.5 A discussion of some identities 83
Comments on Chapter 6 85
7 Some asymptotic laws for multidimensional Brownian motion 87
7.1 Asymptotic windings of planar Brownian motion around n points 88
7.2 Windings of Brownian motion in IR3 90
7.3 Windings of independent planar Brownian motions
around each other 92
7.4 A unified picture of asymptotic windings 93
7.5 The asymptotic distribution of the self linking number
of Brownian motion in H3 94
Comments on Chapter 7 98
8 Some extensions of Paul Levy s arc sine law
for Brownian motion 99
8.1 Some notation 100
8.2 A list of results 101
8.3 A discussion of methods — Some proofs 104
8.4 An excursion theory approach to F. Petit s results 107
8.5 A stochastic calculus approach to P. Petit s results 115
Comments on Chapter 8 117
9 Further results about reflecting Brownian motion
perturbed by its local time at 0 118
9.1 A Ray Knight theorem for the local times of X, up to t^,
and some consequences 118
9.2 Proof of the Ray Knight theorem for the local times of X 120
9.3 Generalisation of a computation of F. Knight 124
9.4 Towards a pathwise decomposition of (Xu, u rf) 128
Comments on Chapter 9 129
Bibliography 131
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| any_adam_object | 1 |
| author | Yor, Marc 1949-2014 |
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| author_facet | Yor, Marc 1949-2014 |
| author_role | aut |
| author_sort | Yor, Marc 1949-2014 |
| author_variant | m y my |
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| bvnumber | BV007924236 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)180637342 (DE-599)BVBBV007924236 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007924236 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:14:19Z |
| institution | BVB |
| isbn | 376432807X 081762807X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005236776 |
| oclc_num | 180637342 |
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| physical | 136 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Lectures in mathematics |
| 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 1 Some special functionals Marc Yor |
| title_fullStr | Some aspects of Brownian motion 1 Some special functionals Marc Yor |
| title_full_unstemmed | Some aspects of Brownian motion 1 Some special functionals Marc Yor |
| title_short | Some aspects of Brownian motion |
| title_sort | some aspects of brownian motion some special functionals |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005236776&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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