Verfügbarkeit: Stochastic differential equations

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Bibliographische Detailangaben
Titel:	Stochastic differential equations
Von:	I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire]
Person:	Gichman, Iosif I. 1918-1985 aut Skorochod, Anatolij V. 1930-2011
Hauptverfassende:	Gichman, Iosif I. 1918-1985 (VerfasserIn), Skorochod, Anatolij V. 1930-2011 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Heidelberg ; New York Springer 1972
Schriftenreihe:	Ergebnisse der Mathematik und ihrer Grenzgebiete Band 72
Schlagworte:	Stochastische Differentialgleichung
Online-Zugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001886196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	VIII, 354 Seiten
ISBN:	3540059466

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adam_text	Table of Contents Introduction ........................ 1 Part I. One-dimensional Stochastic Differential Equations of First Order Chapter 1. Stochastic Integrals and Differentials ........ 7 § 1. The Wiener Process ................. 7 § 2. The Stochastic Integral ............... 11 § 3. Properties of Stochastic Integrals as Function of the Upper Limit ....................... 16 § 4. Stochastic Integrals with Random Limits ........ 27 Chapter 2. The Solutions of Stochastic Differential Equations. . . 33 § 5. Stochastic Differential Equations of First Order ..... 33 § 6. Existence and Uniqueness of the Solutions ....... 39 § 7. Stochastic Equations which Depend on a Parameter ... 50 § 8. Dependence of the Solutions of Stochastic Differential Equations on the Initial Data ............ 59 Chapter 3. Solutions of Stochastic Differential Equations and Mar¬ kov Diffusion Processes ............... 63 § 9. Markov Processes. Diffusion Processes ........ 63 § 10. Diffusion Processes as Solutions of Stochastic Equations . 67 §11. Kolmogorov s Equation ............... 73 § 12. Measures in Function Space Induced by Diffusion Pro¬ cesses ....................... 80 §13. Formulas for Transition Density Functions ....... 91 § 14. Kolmogorov s Equation for the Transition Probability Density ...................... 99 § 15. Time-homogeneous Solutions of Stochastic Differential Equations ..................... 105 Chapter 4. Asymptotic Behavior of the Solutions of Stochastic Equations ..................... 114 § 16. Bounded and Unbounded Solutions of Stochastic Equa¬ tions ....................... 114 § 17. Theorems on the Asymptotic Behavior of Solutions . . . 124 §18. Ergodic Theorems .................. 134 § 19. Stability of Solutions ................ 145 §20. Some Other Limit Theorems ............. 151 Chapter 5. Stochastic Differential Equations on a Finite Spatial Interval ...................... 159 § 21. Boundary Conditions at the Ends of the Interval . . . .159 §22. Processes with Absorption at the Boundary ....... 165 §23. Instantaneous Reflection at the Boundary ....... 178 § 24. Delayed Reflection at the Boundary .......... 193 § 25. Processes with Jump Reflection at the Boundary .... 205 Part П. Systems of Stochastic Differential Equations Chapter 1. Vector Stochastic Differential Equations ....... 215 § 1. Stochastic Line Integrals ............... 216 § 2. Stochastic Line Integrals as Function of the Upper Limit. 232 § 3. Stochastic Differential Equations ........... 237 Chapter 2. Stochastic Differential Equations without After-effect . 245 § 4. Preliminary Remarks ................ 245 § 5. Some Special Types of Stochastic Integrals ....... 247 § 6. The Generalized Ito Formula for Stochastic Differentials 263 § 7. Stochastic Differential Equations without After-effect . . 273 § 8. Stochastic Differential Equations Depending on a Para¬ meter. Diff erentiability w. r. t the Initial Data ..... 275 § 9. Solutions of Stochastic Differential Equations as Markov Processes ..................... 288 § 10. The Distribution of Functional of the Solutions of Stocha¬ stic Differential Equations .............. 300 §11. Some Problems Connected with Homogeneous Stochastic Differential Equations ................ 304 Chapter 3. Asymptotic Behavior of the Solutions of Stochastic Dif¬ ferential Equations .................310 § 12. Stability of Solutions ................310 § 13. Boundedness of the Solutions of Stochastic Differential Equations .....................330 § 14. Limit Theorems for Stochastic Differential Equations . .333 Bibliography ........................348 Index ...........................351
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author	Gichman, Iosif I. 1918-1985 Skorochod, Anatolij V. 1930-2011
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indexdate	2024-12-20T07:57:25Z
institution	BVB
isbn	3540059466
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-001886196
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open_access_boolean
owner	DE-384 DE-19 DE-BY-UBM DE-703 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-83 DE-210
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physical	VIII, 354 Seiten
publishDate	1972
publishDateSearch	1972
publishDateSort	1972
publisher	Springer
record_format	marc
series	Ergebnisse der Mathematik und ihrer Grenzgebiete
series2	Ergebnisse der Mathematik und ihrer Grenzgebiete
spellingShingle	Gichman, Iosif I. 1918-1985 Skorochod, Anatolij V. 1930-2011 Stochastic differential equations Ergebnisse der Mathematik und ihrer Grenzgebiete Stochastische Differentialgleichung (DE-588)4057621-8 gnd
subject_GND	(DE-588)4057621-8
title	Stochastic differential equations
title_alt	Stochasti ceskie differencialnie uravnenija
title_auth	Stochastic differential equations
title_exact_search	Stochastic differential equations
title_full	Stochastic differential equations I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire]
title_fullStr	Stochastic differential equations I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire]
title_full_unstemmed	Stochastic differential equations I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire]
title_short	Stochastic differential equations
title_sort	stochastic differential equations
topic	Stochastische Differentialgleichung (DE-588)4057621-8 gnd
topic_facet	Stochastische Differentialgleichung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001886196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV005871160
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