Lévy processes and stochastic calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2005
|
| Edition: | 1. publ., reprint. |
| Series: | Cambridge studies in advanced mathematics
93 |
| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXIV, 384 S. |
| ISBN: | 0521832632 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lévy processes and stochastic calculus |c David Applebaum |
| 250 | |a 1. publ., reprint. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2005 | |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 93 | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Stochastic integral equations | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface page
ix
Overview
xv
Notation
xxiii
1
Levy processes
1
1.1
Review of measure and probability
1
1.2
Infinite divisibility
20
1.3
Levy processes
39
1.4
Convolution semigroups of probability measures
58
1.55
Some further directions in Levy processes
63
1.6
Notes and further reading
67
1.7
Appendix: An exercise in calculus
69
2
Martingales, stopping times and random measures
70
2.1
Martingales
70
2.2
Stopping times
78
2.3
The jumps of a Levy process
-
Poisson
random measures
86
2.4
The
Lévy-Itô
decomposition
96
2.5
The interlacing construction
111
2.6
Semimartingales
115
2.7
Notes and further reading
1 16
2.8
Appendix:
càdlàg
functions
117
3
Markov processes, semigroups and generators
. 120
3.1
Markov processes, evolutions and semigroups
120
3.2
Semigroups and their generators
129
3.3
Semigroups and generators of Levy processes
136
3.4
L· -Markov semigroups
148
3.5
Lévy-type
operators and the positive maximum principle
156
3.6
Dirichlet forms
164
3.7
Notes and further reading
176
3.8
Appendix: Unbounded operators in Banach spaces
176
4
Stochastic integration
190
4.1
Integrators and integrands
190
4.2
Stochastic integration
197
4.3
Stochastic integrals based on Levy processes
205
4.4
Itô s
formula
218
4.5
Notes and further reading
245
5
Exponential martingales, change of measure and financial
applications
246
5.1
Stochastic exponentials
247
5.2
Exponential martingales
250
5.3
Martingale representation theorems
262
5.4
Stochastic calculus and mathematical finance
267
5.5
Notes and further reading
288
5.6
Appendix: Bessel functions
289
6
Stochastic differential equations
292
6.1
Differential equations and flows
293
6.2
Stochastic differential equations
-
existence and uniqueness
301
6.3
Examples of SDEs
314
6.4
Stochastic flows, cocycle and Markov properties of SDEs
319
6.5
Interlacing for solutions of SDEs
328
6.6
Continuity of solution flows to SDEs
331
6.7
Solutions of SDEs as Feller processes, the Feynman-Kac
formula and martingale problems
337
6.8
Marcus canonical equations
348
6.9
Notes and further reading
357
References
360
Index of notation
375
Subject index
379
|
| adam_txt |
Contents
Preface page
ix
Overview
xv
Notation
xxiii
1
Levy processes
1
1.1
Review of measure and probability
1
1.2
Infinite divisibility
20
1.3
Levy processes
39
1.4
Convolution semigroups of probability measures
58
1.55
Some further directions in Levy processes
63
1.6
Notes and further reading
67
1.7
Appendix: An exercise in calculus
69
2
Martingales, stopping times and random measures
70
2.1
Martingales
70
2.2
Stopping times
78
2.3
The jumps of a Levy process
-
Poisson
random measures
86
2.4
The
Lévy-Itô
decomposition
96
2.5
The interlacing construction
111
2.6
Semimartingales
115
2.7
Notes and further reading
1 16
2.8
Appendix:
càdlàg
functions
117
3
Markov processes, semigroups and generators
. 120
3.1
Markov processes, evolutions and semigroups
120
3.2
Semigroups and their generators
129
3.3
Semigroups and generators of Levy processes
136
3.4
L·"-Markov semigroups
148
3.5
Lévy-type
operators and the positive maximum principle
156
3.6
Dirichlet forms
164
3.7
Notes and further reading
176
3.8
Appendix: Unbounded operators in Banach spaces
176
4
Stochastic integration
190
4.1
Integrators and integrands
190
4.2
Stochastic integration
197
4.3
Stochastic integrals based on Levy processes
205
4.4
Itô's
formula
218
4.5
Notes and further reading
245
5
Exponential martingales, change of measure and financial
applications
246
5.1
Stochastic exponentials
247
5.2
Exponential martingales
250
5.3
Martingale representation theorems
262
5.4
Stochastic calculus and mathematical finance
267
5.5
Notes and further reading
288
5.6
Appendix: Bessel functions
289
6
Stochastic differential equations
292
6.1
Differential equations and flows
293
6.2
Stochastic differential equations
-
existence and uniqueness
301
6.3
Examples of SDEs
314
6.4
Stochastic flows, cocycle and Markov properties of SDEs
319
6.5
Interlacing for solutions of SDEs
328
6.6
Continuity of solution flows to SDEs
331
6.7
Solutions of SDEs as Feller processes, the Feynman-Kac
formula and martingale problems
337
6.8
Marcus canonical equations
348
6.9
Notes and further reading
357
References
360
Index of notation
375
Subject index
379 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:20:30Z |
| indexdate | 2024-07-09T20:26:41Z |
| institution | BVB |
| isbn | 0521832632 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014175051 |
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| physical | XXIV, 384 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| 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 1. publ., reprint. Cambridge [u.a.] Cambridge Univ. Press 2005 XXIV, 384 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 93 Includes bibliographical references and index Lévy processes Stochastic integral equations Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 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 93 (DE-604)BV000003678 93 http://www.loc.gov/catdir/description/cam041/2003063882.html Publisher description http://www.loc.gov/catdir/toc/cam041/2003063882.html Table of contents Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014175051&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 Lévy processes Stochastic integral equations Lévy-Prozess (DE-588)4463623-4 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4463623-4 (DE-588)4057621-8 (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_exact_search_txtP | 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 | Lévy processes Stochastic integral equations Lévy-Prozess (DE-588)4463623-4 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Lévy processes Stochastic integral equations Lévy-Prozess Stochastische Differentialgleichung Stochastisches Integral |
| url | http://www.loc.gov/catdir/description/cam041/2003063882.html http://www.loc.gov/catdir/toc/cam041/2003063882.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014175051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT applebaumdavid levyprocessesandstochasticcalculus |