An introduction to stochastic differential equations:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2013]
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026732753&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026732753&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | viii, 151 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470410544 |
Internformat
MARC
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| 100 | 1 | |a Evans, Lawrence C. |d 1949- |e Verfasser |0 (DE-588)135567777 |4 aut | |
| 245 | 1 | 0 | |a An introduction to stochastic differential equations |c Lawrence C. Evans, Department of Mathematics University of California, Berkeley |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2013] | |
| 264 | 4 | |c © 2013 | |
| 300 | |a viii, 151 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Numerical analysis ... Probabilistic methods, simulation and stochastic differential equations ... Stochastic differential and integral equations |2 msc | |
| 650 | 7 | |a Probability theory and stochastic processes ... Markov processes ... Brownian motion |2 msc | |
| 650 | 7 | |a Probability theory and stochastic processes ... Stochastic analysis ... Stochastic ordinary differential equations |2 msc | |
| 650 | 7 | |a Numerical analysis ... Partial differential equations, boundary value problems ... Probabilistic methods, particle methods, etc. |2 msc | |
| 650 | 4 | |a Stochastic differential equations | |
| 650 | 4 | |a Numerical analysis ... Probabilistic methods, simulation and stochastic differential equations ... Stochastic differential and integral equations | |
| 650 | 4 | |a Probability theory and stochastic processes ... Markov processes ... Brownian motion | |
| 650 | 4 | |a Probability theory and stochastic processes ... Stochastic analysis ... Stochastic ordinary differential equations | |
| 650 | 4 | |a Numerical analysis ... Partial differential equations, boundary value problems ... Probabilistic methods, particle methods, etc. | |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 606f 2014 B 676 0202 MAT 606f 2014 A 5290 |
|---|---|
| DE-BY-TUM_katkey | 1958233 |
| DE-BY-TUM_location | 01 02 |
| DE-BY-TUM_media_number | 040080398243 040080097250 |
| _version_ | 1821934815361892352 |
| adam_text | CONTENTS
Preface vii
Chapter
1.
Introduction
1
§1.1.
Deterministic and random differential equations
1
§1.2.
Stochastic differentials
2
§1.3.
Itô s
chain rule
3
Chapter
2.
A Crash Course
m
Probability Theory
7
§2.1.
Basic definitions
7
§2.2.
Expected value, variance
14
§2.3.
Independence
17
§2.4.
Some probabilistic methods
21
§2.5.
Law of Large Numbers, Central Limit Theorem
23
§2.6.
Conditional expectation
28
§2.7.
Martingales
34
Chapter
3.
Browman Motion and White Noise
37
§3.1.
Motivation
37
§3.2.
Definition, elementary properties
41
§3.3.
Construction of Browman motion
45
§3.4.
Sample path properties
53
§3.5.
Markov property
57
vi
CONTENTS
Chapter
4.
Stochastic Integrals
59
§4.].
Preliminaries
59
§4.2.
Itô s
integral
65
§4.3.
Itô s
chain and product rules
70
§4.4.
Itô s
integral in higher dimensions
77
Chapter
5.
Stochastic Differential Equations
83
§5.1.
Definitions, examples
83
§5.2.
Existence and uniqueness of solutions
90
§5.3.
Properties of solutions
96
§5.4.
Linear stochastic differential equations
98
Chapter
6.
Applications
103
§6.1.
Stopping times
103
§6.2.
Applications to PDE, Feynman-Kac formula
108
§6.3.
Optimal stopping
112
§6.4.
Options pricing
117
§6.5.
The Stratonovich integral
121
Appendix
127
Exercises
135
Notes and Suggested Reading
145
Bibliography
147
Index
149
This short book provides a quick, but very readable introduction to stochastic differential
equations, that is, to differential equations subject to additive white noise and related
random disturbances. The exposition is concise and strongly focused upon the interplay
between probabilistic intuition and mathematical ngor. Topics include a quick survey of
measure theoretic probability theory, followed by an introduction to Brownian motion and
the
Ito
stochastic calculus, and finally the theory of stochastic differential equations. The
text also includes applications to partial differential equations, optimal stopping problems
and options pricing.
This book can be used as a text for senior undergraduates or beginning graduate students in
mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn
the basics of stochastic differential equations. The reader is assumed to be fairly familiar
with measure theoretic mathematical analysis, but is not assumed to have any particular
knowledge of probability theory (which is rapidly developed in Chapter
2
of the book).
|
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| illustrated | Illustrated |
| indexdate | 2024-12-20T16:44:07Z |
| institution | BVB |
| isbn | 9781470410544 |
| language | English |
| lccn | 013024818 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026732753 |
| oclc_num | 859552823 |
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| physical | viii, 151 Seiten Illustrationen, Diagramme |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | American Mathematical Society |
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| spellingShingle | Evans, Lawrence C. 1949- An introduction to stochastic differential equations Numerical analysis ... Probabilistic methods, simulation and stochastic differential equations ... Stochastic differential and integral equations msc Probability theory and stochastic processes ... Markov processes ... Brownian motion msc Probability theory and stochastic processes ... Stochastic analysis ... Stochastic ordinary differential equations msc Numerical analysis ... Partial differential equations, boundary value problems ... Probabilistic methods, particle methods, etc. msc Stochastic differential equations Numerical analysis ... Probabilistic methods, simulation and stochastic differential equations ... Stochastic differential and integral equations Probability theory and stochastic processes ... Markov processes ... Brownian motion Probability theory and stochastic processes ... Stochastic analysis ... Stochastic ordinary differential equations Numerical analysis ... Partial differential equations, boundary value problems ... Probabilistic methods, particle methods, etc. Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 |
| title | An introduction to stochastic differential equations |
| title_auth | An introduction to stochastic differential equations |
| title_exact_search | An introduction to stochastic differential equations |
| title_full | An introduction to stochastic differential equations Lawrence C. Evans, Department of Mathematics University of California, Berkeley |
| title_fullStr | An introduction to stochastic differential equations Lawrence C. Evans, Department of Mathematics University of California, Berkeley |
| title_full_unstemmed | An introduction to stochastic differential equations Lawrence C. Evans, Department of Mathematics University of California, Berkeley |
| title_short | An introduction to stochastic differential equations |
| title_sort | an introduction to stochastic differential equations |
| topic | Numerical analysis ... Probabilistic methods, simulation and stochastic differential equations ... Stochastic differential and integral equations msc Probability theory and stochastic processes ... Markov processes ... Brownian motion msc Probability theory and stochastic processes ... Stochastic analysis ... Stochastic ordinary differential equations msc Numerical analysis ... Partial differential equations, boundary value problems ... Probabilistic methods, particle methods, etc. msc Stochastic differential equations Numerical analysis ... Probabilistic methods, simulation and stochastic differential equations ... Stochastic differential and integral equations Probability theory and stochastic processes ... Markov processes ... Brownian motion Probability theory and stochastic processes ... Stochastic analysis ... Stochastic ordinary differential equations Numerical analysis ... Partial differential equations, boundary value problems ... Probabilistic methods, particle methods, etc. Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Numerical analysis ... Probabilistic methods, simulation and stochastic differential equations ... Stochastic differential and integral equations Probability theory and stochastic processes ... Markov processes ... Brownian motion Probability theory and stochastic processes ... Stochastic analysis ... Stochastic ordinary differential equations Numerical analysis ... Partial differential equations, boundary value problems ... Probabilistic methods, particle methods, etc. Stochastic differential equations Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026732753&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026732753&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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