Lévy processes and stochastic calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 2. ed. |
| Series: | Cambridge studies in advanced mathematics
116 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXX, 460 S. |
| ISBN: | 0521738652 9780521738651 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lévy processes and stochastic calculus |c David Applebaum |
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Record in the Search Index
| _version_ | 1804139344225632256 |
|---|---|
| adam_text | Contents
Preface
to Second Edition
page
xiii
Preface
XV
Overview
xxi
Notation
xxix
1
Levy processes
1
1.1
Review of measure and probability
1
1.2
Infinite divisibility
21
1.3
Levy processes
43
1.4
Convolution semigroups of probability measures
62
1.5
Some further directions in Levy processes
67
1.6
Notes and further reading
78
1.7
Appendix: An exercise in calculus
80
2
Martingales, stopping times and random measures
82
2.1
Martingales
83
2.2
Stopping times
91
2.3
The jumps of a Levy process
-
Poisson
random
measures
99
2.4
The
Lévy-Itô
decomposition
112
2.5
Moments of Levy Processes
131
2.6
The interlacing construction
133
2.7
Semimartingales
137
2.8
Notes and further reading
138
2.9
Appendix:
càdlàg
functions
139
2.10
ADDendix: Unitary action of the shift
141
3
Markov processes, semigroups and generators
143
3.1
Markov processes, evolutions
and semigroups
143
3.2
Semigroups and their generators
153
3.3
Semigroups and generators of Levy processes
160
3.4
II-Markov semigroups
172
3.5
Lévy-type
operators and the positive
maximum principle
180
3.6
Dirichlet forms
189
3.7
Notes and further reading
200
3.8
Appendix: Unbounded operators in Banach spaces
201
4
Stochastic integration
214
4.1
Integrators and integrands
214
4.2
Stochastic integration
221
4.3
Stochastic integrals based on Levy processes
229
4.4
Itô s
formula
243
4.5
Notes and further reading
279
5
Exponential martingales, change of measure and financial
applications
280
5.1
Stochastic exponentials
281
5.2
Exponential martingales
285
5.3
Martingale representation theorems
299
5.4
Multiple
Wiener-Lévy
Integrals
306
5.5
Introduction to Malliavin Calculus
317
5.6
Stochastic calculus and mathematical finance
324
5.7
Notes and further reading
348
5.8
Appendix: Bessel functions
348
5.9
Appendix: A density result
351
6
Stochastic differential equations
354
6.1
Differential equations and flows
355
6.2
Stochastic differential equations
-
existence and uniqueness
363
6.3
Examples of SDEs
377
6.4
Stochastic flows, cocycle and Markov properties of SDEs
383
6.5
Interlacing for solutions of SDEs
392
6.6
Continuity of solution flows to SDEs
395
6.7
Solutions of SDEs as Feller processes, the
Feynman-Kac formula and martingale problems
399
Contents xi
6.8 Lyapunov
exponents for stochastic
differential equations
411
6.9
Densities for Solutions of SDEs
415
6.10
Marcus canonical equations
417
6.11
Notes and further reading
426
References
431
Index of notation
449
Subject index
454
|
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| classification_rvk | SK 820 |
| classification_tum | MAT 605f MAT 607f |
| ctrlnum | (OCoLC)440766110 (DE-599)BVBBV035656204 |
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| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035656204 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:42:35Z |
| institution | BVB |
| isbn | 0521738652 9780521738651 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017710698 |
| oclc_num | 440766110 |
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| owner_facet | DE-739 DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-824 DE-83 DE-523 |
| physical | XXX, 460 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Applebaum, David 1956- Verfasser (DE-588)136277659 aut Lévy processes and stochastic calculus David Applebaum 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2009 XXX, 460 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 116 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 s DE-604 Stochastisches Integral (DE-588)4126478-2 s Stochastische Differentialgleichung (DE-588)4057621-8 s Cambridge studies in advanced mathematics 116 (DE-604)BV000003678 116 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017710698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Applebaum, David 1956- Lévy processes and stochastic calculus Cambridge studies in advanced mathematics Stochastische Differentialgleichung (DE-588)4057621-8 gnd Lévy-Prozess (DE-588)4463623-4 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4463623-4 (DE-588)4126478-2 |
| title | Lévy processes and stochastic calculus |
| title_auth | Lévy processes and stochastic calculus |
| title_exact_search | Lévy processes and stochastic calculus |
| title_full | Lévy processes and stochastic calculus David Applebaum |
| title_fullStr | Lévy processes and stochastic calculus David Applebaum |
| title_full_unstemmed | Lévy processes and stochastic calculus David Applebaum |
| title_short | Lévy processes and stochastic calculus |
| title_sort | levy processes and stochastic calculus |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Lévy-Prozess (DE-588)4463623-4 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Stochastische Differentialgleichung Lévy-Prozess Stochastisches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017710698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT applebaumdavid levyprocessesandstochasticcalculus |