Verfügbarkeit: Asymptotic methods for the Fokker-Planck equation and the exit problem in applications

Asymptotic methods for the Fokker-Planck equation and the exit problem in applications:

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Bibliographische Detailangaben
Beteiligte Personen:	Grasman, Johan 1944- (VerfasserIn), Van Herwaarden, Onno A. 1956- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 1999
Schriftenreihe:	Springer series in synergetics
Schlagwörter:	Fokker-Planck equation > Asymptotic theory Perturbation (Mathematics) Stochastic analysis Stochastische Analysis Fokker-Planck-Gleichung Asymptotische Methode Störungstheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008337092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	IX, 220 S. graph. Darst.
ISBN:	3540644350

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CONTENTS PART I THE FOKKER-PLANCK EQUATION 1. DYNAMICAL SYSTEMS PERTURBED BY NOISE: THE LANGEVIN EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 STOCHASTIC PROCESSES AND THE EFFECT OF SMALL NOISE . . . . . . . . . . . 3 1.2 THE IT ^ O CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 SMALL NOISE EXPANSION OF THE LANGEVIN EQUATION . . . . . . . . . . . . 10 1.4 SIMULATION OF THE STOCHASTIC PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2. THE FOKKER-PLANCK EQUATION: FIRST EXIT FROM A DOMAIN . . . . . . 18 2.1 THE FORWARD AND THE BACKWARD EQUATION . . . . . . . . . . . . . . . . . . . . 18 2.2 THE EXIT PROBABILITY AND THE EXPECTED EXIT TIME . . . . . . . . . . . . 23 2.3 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3. THE FOKKER-PLANCK EQUATION: ONE DIMENSION . . . . . . . . . . . . . . . . . 27 3.1 STATIONARY AND QUASI-STATIONARY DISTRIBUTIONS . . . . . . . . . . . . . . . 28 3.2 EXIT TIME AND EXIT PROBABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 PART II ASYMPTOTIC SOLUTION OF THE EXIT PROBLEM 4. SINGULAR PERTURBATION ANALYSIS OF THE DIFFERENTIAL EQUATIONS FOR THE EXIT PROBABILITY AND EXIT TIME IN ONE DIMENSION . . . . . . 43 4.1 THE EXIT PROBABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 THE EXPECTED EXIT TIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3 VANISHING DIFFUSION AND DRIFT AT A BOUNDARY . . . . . . . . . . . . . . . . . 52 4.4 THE PROBLEM OF UNLIKELY EXIT USING THE WKB-METHOD . . . . . . 57 4.5 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 VIII CONTENTS 5. THE FOKKER-PLANCK EQUATION IN SEVERAL DIMENSIONS: THE ASYMPTOTIC EXIT PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.1 EXIT BY DIFFUSION ACROSS THE DRIFT . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.2 EXIT BY DIFFUSION ALONG THE DRIFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3 EXIT HY DIFFUSION AGAINST THE DRIFT . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.4 EXIT FROM THE DOMAIN OF ATTRACTION . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.5 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 PART III APPLICATIONS 6. DISPERSIVE GROUNDWATER FLOW AND POLLUTION . . . . . . . . . . . . . . . . . . . . 99 6.1 THE BOUNDARY LAYER FOR A SYMMETRIC FLOW FIELD . . . . . . . . . . . 101 6.2 THE BOUNDARY LAYER FOR AN ARBITRARY FLOW FIELD . . . . . . . . . . . 107 7. EXTINCTION IN SYSTEMS OF INTERACTING BIOLOGICAL POPULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.1 A PREY-PREDATOR SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2 THE SIR-MODEL IN STOCHASTIC EPIDEMIOLOGY . . . . . . . . . . . . . . . . 130 7.3 EXTINCTION OF A POPULATION WITHIN A SYSTEM OF INTERACTING POPULATIONS . . . . . . . . . . . . . . . . . 141 8. STOCHASTIC OSCILLATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.1 EQUIVALENT STATISTICAL LINEARIZATION . . . . . . . . . . . . . . . . . . . . . . . . . 150 8.2 ALMOST LINEAR OSCILLATION AND STOCHASTIC AVERAGING . . . . . . . . 152 8.3 STOCHASTIC RELAXATION OSCILLATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 9. CONFIDENCE DOMAIN, RETURN TIME AND CONTROL . . . . . . . . . . . . . . . . 168 9.1 CONFIDENCE DOMAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 9.2 RETUM TIME OF A STOCHASTIC SYSTEM AND ITS APPLICATION IN ECOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9.3 APPLICATIONS IN CONTROL THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 10. A MARKOV CHAIN APPROXIMATION OF THE STOCHASTIC DYNAMICAL SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 10.1 PREFERENT STATES IN A LOW ORDER SPECTRAL MODEL OF THE ATMOSPHERIC CIRCULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 10.2 EXTINCTION AND RECOLONIZATION IN POPULATION BIOLOGY . . . . . . . 192 CONTENTS IX LITERATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 ANSWERS TO EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 AUTHOR INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 SUBJECT INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
any_adam_object	1
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spellingShingle	Grasman, Johan 1944- Van Herwaarden, Onno A. 1956- Asymptotic methods for the Fokker-Planck equation and the exit problem in applications Fokker-Planck equation Asymptotic theory Perturbation (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Fokker-Planck-Gleichung (DE-588)4126333-9 gnd Asymptotische Methode (DE-588)4287476-2 gnd Störungstheorie (DE-588)4128420-3 gnd
subject_GND	(DE-588)4132272-1 (DE-588)4126333-9 (DE-588)4287476-2 (DE-588)4128420-3
title	Asymptotic methods for the Fokker-Planck equation and the exit problem in applications
title_auth	Asymptotic methods for the Fokker-Planck equation and the exit problem in applications
title_exact_search	Asymptotic methods for the Fokker-Planck equation and the exit problem in applications
title_full	Asymptotic methods for the Fokker-Planck equation and the exit problem in applications J. Grasman ; O. A. VanHerwaarden
title_fullStr	Asymptotic methods for the Fokker-Planck equation and the exit problem in applications J. Grasman ; O. A. VanHerwaarden
title_full_unstemmed	Asymptotic methods for the Fokker-Planck equation and the exit problem in applications J. Grasman ; O. A. VanHerwaarden
title_short	Asymptotic methods for the Fokker-Planck equation and the exit problem in applications
title_sort	asymptotic methods for the fokker planck equation and the exit problem in applications
topic	Fokker-Planck equation Asymptotic theory Perturbation (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Fokker-Planck-Gleichung (DE-588)4126333-9 gnd Asymptotische Methode (DE-588)4287476-2 gnd Störungstheorie (DE-588)4128420-3 gnd
topic_facet	Fokker-Planck equation Asymptotic theory Perturbation (Mathematics) Stochastic analysis Stochastische Analysis Fokker-Planck-Gleichung Asymptotische Methode Störungstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008337092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT grasmanjohan asymptoticmethodsforthefokkerplanckequationandtheexitprobleminapplications AT vanherwaardenonnoa asymptoticmethodsforthefokkerplanckequationandtheexitprobleminapplications

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