Introduction to stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2006
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Beschreibung für Leser Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 234 S. Ill. 25 cm |
| ISBN: | 158488651X |
Internformat
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| 100 | 1 | |a Lawler, Gregory F. |d 1955- |e Verfasser |0 (DE-588)123908671 |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic processes |c Gregory F. Lawler |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2006 | |
| 300 | |a XIII, 234 S. |b Ill. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Processos estocásticos |2 larpcal | |
| 650 | 4 | |a Stokastik işlemler | |
| 650 | 4 | |a Stochastic processes | |
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Datensatz im Suchindex
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| adam_text |
Contents
Preface
to Second Edition
ix
Preface to First Edition
xi
0
Preliminaries
1
0.1
Introduction
. 1
0.2
Linear Differential Equations
. 1
0.3
Linear Difference Equations
. 3
0.4
Exercises
. 6
1
Finite Markov Chains
9
1.1
Definitions and Examples
. 9
1.2
Large-Time Behavior and Invariant Probability
. 14
1.3
Classification of States
. 17
1.3.1
Reducibility
. 19
1.3.2
Periodicity
. 21
1.3.3
Irreducible, aperiodic chains
. 22
1.3.4
Reducible or periodic chains
. 22
1.4
Return Times
. 24
1.5
Transient States
. 26
1.6
Examples
. 31
1.7
Exercises
. 35
2
Countable Markov Chains
43
2.1
Introduction
. 43
2.2
Recurrence and Transience
. 45
2.3
Positive Recurrence and Null Recurrence
. 50
2.4
Branching Process
. 53
2.5
Exercises
. 57
3
Continuous-Time Markov Chains
65
3.1
Poisson
Process
. 65
3.2
Finite State Space
. 68
3.3
Birth-and-Death Processes
. 74
3.4
General Case
. 81
3.5
Exercises
. 82
Optimal
Stopping
87
4.1 Optimal
Stopping of Markov Chains
. 87
4.2
Optimal Stopping with Cost
. 93
4.3
Optimal Stopping with Discounting
. 96
4.4
Exercises
. 98
Martingales
101
5.1
Conditional Expectation
. 101
5.2
Definition and Examples
. 106
5.3
Optional Sampling Theorem
. 110
5.4
Uniform Integrability
. 114
5.5
Martingale Convergence Theorem
. 116
5.6
Maximal Inequalities
. 122
5.7
Exercises
. 125
Renewal Processes
131
6.1
Introduction
. 131
6.2
Renewal Equation
. 136
6.3
Discrete Renewal Processes
. 144
6.4
M/G/l and G/M/l Queues
. 148
6.5
Exercises
. 151
Reversible Markov Chains
155
7.1
Reversible Processes
. 155
7.2
Convergence to Equilibrium
. 157
7.3
Markov Chain Algorithms
. 162
7.4
A Criterion for Recurrence
. 166
7.5
Exercises
. 170
Brownian Motion
173
8.1
Introduction
. 173
8.2
Markov Property
. 176
8.3
Zero Set of Brownian Motion
. 181
8.4
Brownian Motion in Several Dimensions
. 184
8.5
Recurrence and Transience
. 189
8.6
Fractal Nature of Brownian Motion
. 191
8.7
Scaling Rules
. 192
8.8
Brownian Motion with Drift
. 193
8.9
Exercises
. 195
Stochastic Integration
199
9.1
Integration with Respect to Random Walk
. 199
9.2
Integration with Respect to Brownian Motion
. 200
9.3
Itô's
Formula
. 205
9.4
Extensions of
Itô's
Formula
. 209
9.5
Continuous Martingales
. 216
9.6
Girsanov Transformation
. 218
9.7
Feynman-Kac Formula
. 221
9.8
Black-Scholes Formula
. 223
9.9
Simulation
. 228
9.10
Exercises
. 228
Suggestions for Further Reading
231
Index
233
Focusing on mathematical ideas rather than proofs, Introduction to
Stochastic Processes, Second Edition provides quick access to
important foundations of probability theory applicable to problems
in many fields. Approaching all problems and theorems without any
measure theory, the book provides a concise and informal introduction
to stochastic processes evolving with time.
Here's what's new in the Second Edition:
•
Expanded chapter on stochastic integration that introduces modern
mathematical finance
•
Expanded discussion of
Itô's
formula including Girsanov theory,
the Feynman-Kac formula, and the Black-Scholes formula in
stochastic integration
•
New topics such as Doob's maximal inequality and a discussion
on self similarity in the chapter on Brownian motion
This concise, informal introduction is designed to meet the needs of
students and professionals not only in mathematics and statistics, but
in the many fields in which the concepts presented are also important,
including computer science, economics, business, biological sciences,
psychology, and engineering. It acquaints readers with the possibilities
of applying stochastic processes in their work. |
| adam_txt |
Contents
Preface
to Second Edition
ix
Preface to First Edition
xi
0
Preliminaries
1
0.1
Introduction
. 1
0.2
Linear Differential Equations
. 1
0.3
Linear Difference Equations
. 3
0.4
Exercises
. 6
1
Finite Markov Chains
9
1.1
Definitions and Examples
. 9
1.2
Large-Time Behavior and Invariant Probability
. 14
1.3
Classification of States
. 17
1.3.1
Reducibility
. 19
1.3.2
Periodicity
. 21
1.3.3
Irreducible, aperiodic chains
. 22
1.3.4
Reducible or periodic chains
. 22
1.4
Return Times
. 24
1.5
Transient States
. 26
1.6
Examples
. 31
1.7
Exercises
. 35
2
Countable Markov Chains
43
2.1
Introduction
. 43
2.2
Recurrence and Transience
. 45
2.3
Positive Recurrence and Null Recurrence
. 50
2.4
Branching Process
. 53
2.5
Exercises
. 57
3
Continuous-Time Markov Chains
65
3.1
Poisson
Process
. 65
3.2
Finite State Space
. 68
3.3
Birth-and-Death Processes
. 74
3.4
General Case
. 81
3.5
Exercises
. 82
Optimal
Stopping
87
4.1 Optimal
Stopping of Markov Chains
. 87
4.2
Optimal Stopping with Cost
. 93
4.3
Optimal Stopping with Discounting
. 96
4.4
Exercises
. 98
Martingales
101
5.1
Conditional Expectation
. 101
5.2
Definition and Examples
. 106
5.3
Optional Sampling Theorem
. 110
5.4
Uniform Integrability
. 114
5.5
Martingale Convergence Theorem
. 116
5.6
Maximal Inequalities
. 122
5.7
Exercises
. 125
Renewal Processes
131
6.1
Introduction
. 131
6.2
Renewal Equation
. 136
6.3
Discrete Renewal Processes
. 144
6.4
M/G/l and G/M/l Queues
. 148
6.5
Exercises
. 151
Reversible Markov Chains
155
7.1
Reversible Processes
. 155
7.2
Convergence to Equilibrium
. 157
7.3
Markov Chain Algorithms
. 162
7.4
A Criterion for Recurrence
. 166
7.5
Exercises
. 170
Brownian Motion
173
8.1
Introduction
. 173
8.2
Markov Property
. 176
8.3
Zero Set of Brownian Motion
. 181
8.4
Brownian Motion in Several Dimensions
. 184
8.5
Recurrence and Transience
. 189
8.6
Fractal Nature of Brownian Motion
. 191
8.7
Scaling Rules
. 192
8.8
Brownian Motion with Drift
. 193
8.9
Exercises
. 195
Stochastic Integration
199
9.1
Integration with Respect to Random Walk
. 199
9.2
Integration with Respect to Brownian Motion
. 200
9.3
Itô's
Formula
. 205
9.4
Extensions of
Itô's
Formula
. 209
9.5
Continuous Martingales
. 216
9.6
Girsanov Transformation
. 218
9.7
Feynman-Kac Formula
. 221
9.8
Black-Scholes Formula
. 223
9.9
Simulation
. 228
9.10
Exercises
. 228
Suggestions for Further Reading
231
Index
233
Focusing on mathematical ideas rather than proofs, Introduction to
Stochastic Processes, Second Edition provides quick access to
important foundations of probability theory applicable to problems
in many fields. Approaching all problems and theorems without any
measure theory, the book provides a concise and informal introduction
to stochastic processes evolving with time.
Here's what's new in the Second Edition:
•
Expanded chapter on stochastic integration that introduces modern
mathematical finance
•
Expanded discussion of
Itô's
formula including Girsanov theory,
the Feynman-Kac formula, and the Black-Scholes formula in
stochastic integration
•
New topics such as Doob's maximal inequality and a discussion
on self similarity in the chapter on Brownian motion
This concise, informal introduction is designed to meet the needs of
students and professionals not only in mathematics and statistics, but
in the many fields in which the concepts presented are also important,
including computer science, economics, business, biological sciences,
psychology, and engineering. It acquaints readers with the possibilities
of applying stochastic processes in their work. |
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| index_date | 2024-07-02T15:51:28Z |
| indexdate | 2024-08-31T00:24:10Z |
| institution | BVB |
| isbn | 158488651X |
| language | English |
| lccn | 2006040208 |
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| spelling | Lawler, Gregory F. 1955- Verfasser (DE-588)123908671 aut Introduction to stochastic processes Gregory F. Lawler 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2006 XIII, 234 S. Ill. 25 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Processos estocásticos larpcal Stokastik işlemler Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Stochastischer Prozess (DE-588)4057630-9 s DE-604 http://www.loc.gov/catdir/enhancements/fy0654/2006040208-d.html Beschreibung für Leser Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015024843&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015024843&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Lawler, Gregory F. 1955- Introduction to stochastic processes Processos estocásticos larpcal Stokastik işlemler Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4151278-9 |
| title | Introduction to stochastic processes |
| title_auth | Introduction to stochastic processes |
| title_exact_search | Introduction to stochastic processes |
| title_exact_search_txtP | Introduction to stochastic processes |
| title_full | Introduction to stochastic processes Gregory F. Lawler |
| title_fullStr | Introduction to stochastic processes Gregory F. Lawler |
| title_full_unstemmed | Introduction to stochastic processes Gregory F. Lawler |
| title_short | Introduction to stochastic processes |
| title_sort | introduction to stochastic processes |
| topic | Processos estocásticos larpcal Stokastik işlemler Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Processos estocásticos Stokastik işlemler Stochastic processes Stochastischer Prozess Einführung |
| url | http://www.loc.gov/catdir/enhancements/fy0654/2006040208-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015024843&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=015024843&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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