Verfügbarkeit: Stochastic processes | Technische Universität München

Stochastic processes:

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Bibliographische Detailangaben
Beteilige Person:	Varadhan, S. R. S. 1940- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY Courant Inst. of Math. Sciences [u.a.] 2007
Schriftenreihe:	Courant lecture notes in mathematics 16
Schlagwörter:	Processos estocásticos Processus stochastiques Stochastic processes Stochastischer Prozess
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016226434&sequence=000002&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=016226434&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	IX, 126 S.
ISBN:	9780821840856

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface ix Chapter 1. Introduction 1 1.1. Continuous Time Processes 1 1.2. Continuous Parameter Martingales 3 1.3. Semimartingales 8 1.4. Martingales and Stochastic Integrals 10 Chapter 2. Processes with Independent Increments 13 2.1. The Basic Poisson Process 13 2.2. Compound Poisson Processes 16 2.3. Infinite Number of Small Jumps 17 2.4. Infinitesimal Generators 20 2.5. Some Associated Martingales 21 Chapter 3. Poisson Point Processes 25 3.1. Point Processes 25 3.2. Poisson Point Process 26 Chapter 4. Jump Markov Processes 29 4.1. Simple Examples 29 4.2. Semigroups of Operators 31 4.3. Example: Birth and Death Processes 34 4.4. Markov Processes and Martingales 35 4.5. Explosion 39 4.6. Recurrence and Transience 44 4.7. Invariant Distributions 45 4.8. Beyond Explosion 47 Chapter 5. Brownian Motion 49 5.1. Definition of Brownian Motion 49 5.2. Markov and Strong Markov Property 51 5.3. Heat Equation 53 5.4. Recurrence 55 5.5. Feynman-Kac Formula 56 5.6. Arcsine Law 57 5.7. Harmonic Oscillator 59 5.8. Exit Times from Bounded Intervals 60 viü CONTENTS 5.9. Stochastic Integrals 61 5.10. Brownian Motion with a Drift, Girsanov Formula 69 5.11. Ornstein-Uhlenbeck Process 72 5.12. Invariant Densities 75 5.13. Local Times 76 5.14. Reflected Brownian Motion 79 5.15. Excursion Theory 81 5.16. Invariance Principle 83 5.17. Representation of Martingales 85 Chapter 6. One-Dimensional Diffusions 87 6.1. Stochastic Differential Equations 87 6.2. Properties of the Solution 90 6.3. Connections with Differential Equations 94 6.4. Martingale Characterization 97 6.5. Random Time Change 99 6.6. Some Examples 100 Chapter 7. General Theory of Markov Processes 107 7.1. Introduction 107 7.2. Semigroups, Generators and Resolvents 108 7.3. Generators and Martingales 110 7.4. Invariant Measures and Ergodic Theory 111 Appendix A. Measures on Polish Spaces 113 A.I. The Space C[0, 1] 116 A.2. The Space D[0, 1] 118 Appendix B. Additional Remarks 121 Bibliography 123 Index 125 This is a brief introduction to stochastic processes studying certain elementary continuous-time processes. After a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps, the author proceeds to introduce Brownian motion and to develop stochastic integrals and Ito s theory in the context of one-dimensional diffusion processes. The book ends with a brief survey of the general theory of Markov processes. The book is based on courses given by the author at the Courant Institute and can be used as a sequel to the author s successful book Probability in this series.
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spellingShingle	Varadhan, S. R. S. 1940- Stochastic processes Courant lecture notes in mathematics Processos estocásticos larpcal Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd
subject_GND	(DE-588)4057630-9
title	Stochastic processes
title_auth	Stochastic processes
title_exact_search	Stochastic processes
title_full	Stochastic processes S. R. S. Varadhan
title_fullStr	Stochastic processes S. R. S. Varadhan
title_full_unstemmed	Stochastic processes S. R. S. Varadhan
title_short	Stochastic processes
title_sort	stochastic processes
topic	Processos estocásticos larpcal Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd
topic_facet	Processos estocásticos Processus stochastiques Stochastic processes Stochastischer Prozess
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