Verfügbarkeit: Multidimensional diffusion processes | Technische Universität München

Multidimensional diffusion processes:

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Bibliographische Detailangaben
Beteiligte Personen:	Stroock, Daniel W. 1940- (VerfasserIn), Varadhan, S. R. S. 1940- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin u.a. Springer 1997
Ausgabe:	Corr. 2. print.
Schriftenreihe:	Die Grundlehren der mathematischen Wissenschaften 233
Schlagwörter:	Diffusion processes Stochastik Diffusionsprozess Diffusion Martingal Markov-Prozess
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007692407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XII, 338 S. graph. Darst.
ISBN:	0387903534 3540903534

Internformat

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Datensatz im Suchindex

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adam_text	Contents Frequently Used Notation xi Chapter 0. Introduction 1 Chapter 1. Preliminary Material: Extension Theorems, Martingales, and Compactness 7 1.0 Introduction 7 1.1 Weak Convergence, Conditional Probability Distributions and Extension Theorems 7 1.2 Martingales 19 1.3 The Space C([0, oo); Rd) 30 1.4 Martingales and Compactness 36 1.5 Exercises 42 Chapter 2. Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure 46 2.1 Regularity of Paths 46 2.2 Markov Processes and Transition Probabilities 51 2.3 Wiener Measure 56 2.4 Exercises 60 Chapter 3. Parabolic Partial Differential Equations 65 3.1 The Maximum Principle 65 3.2 Existence Theorems 71 3.3 Exercises 79 Chapter 4. The Stochastic Calculus of Diffusion Theory 82 4.1 Brownian Motion 82 4.2 Equivalence of Certain Martingales 85 4.3 Ito Processes and Stochastic Integration 92 4.4 Ito s Formula 104 4.5 Ito Processes as Stochastic Integrals 107 4.6 Exercises Ill Chapter 5. Stochastic Differential Equations 122 5.0 Introduction 122 5.1 Existence and Uniqueness 124 Viii Contents 5.2 On the Lipschitz Condition 131 5.3 Equivalence of Different Choices of the Square Root 132 5.4 Exercises 134 Chapter 6. The Martingale Formulation 136 6.0 Introduction 136 6.1 Existence 139 6.2 Uniqueness: Markov Property 145 6.3 Uniqueness: Some Examples 149 6.4 Cameron Martin Girsanov Formula 152 6.5 Uniqueness: Random Time Change 157 6.6 Uniqueness: Localization 161 6.7 Exercises 165 Chapter 7. Uniqueness , 171 7.0 Introduction 171 7.1 Uniqueness: Local Case 174 7.2 Uniqueness: Global Case 187 7.3 Exercises 190 Chapter 8. Ito s Uniqueness and Uniqueness to the Martingale Problem . . 195 8.0 Introduction 195 8.1 Results of Yamada and Watanabe 195 8.2 More on Ito Uniqueness 204 8.3 Exercises 207 Chapter 9. Some Estimates on the Transition Probability Functions 208 9.0 Introduction 208 9.1 The Inhomogeneous Case 209 9.2 The Homogeneous Case 233 Chapter 10. Explosion 248 10.0 Introduction 248 10.1 Locally Bounded Coefficients 249 10.2 Conditions for Explosion and Non Explosion 254 10.3 Exercises 259 Chapter 11. Limit Theorems 261 11.0 Introduction 261 11.1 Convergence of Diffusion Process 262 11.2 Convergence of Markov Chains to Diffusions 266 11.3 Convergence of Diffusion Processes: Elliptic Case 272 11.4 Convergence of Transition Probability Densities 279 11.5 Exercises 283 Chapter 12. The Non Unique Case 285 12.0 Introduction 285 12.1 Existence of Measurable Choices 286 12.2 Markov Selections 290 Contents ix 12.3 Reconstruction of All Solutions 296 12.4 Exercises 302 Appendix 304 A.O Introduction 304 A.I Lp Estimates for Some Singular Integral Operators 306 A.2 Proof of the Main Estimate 315 A.3 Exercises 323 Bibliographical Remarks 328 Bibliography 331 Index 337
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illustrated	Illustrated
indexdate	2024-12-20T10:12:27Z
institution	BVB
isbn	0387903534 3540903534
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-007692407
oclc_num	35029577
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owner_facet	DE-91G DE-BY-TUM DE-20 DE-384 DE-706 DE-11 DE-M347 DE-83
physical	XII, 338 S. graph. Darst.
publishDate	1997
publishDateSearch	1997
publishDateSort	1997
publisher	Springer
record_format	marc
series	Die Grundlehren der mathematischen Wissenschaften
series2	Die Grundlehren der mathematischen Wissenschaften
spellingShingle	Stroock, Daniel W. 1940- Varadhan, S. R. S. 1940- Multidimensional diffusion processes Die Grundlehren der mathematischen Wissenschaften Diffusion processes Stochastik (DE-588)4121729-9 gnd Diffusionsprozess (DE-588)4274463-5 gnd Diffusion (DE-588)4012277-3 gnd Martingal (DE-588)4126466-6 gnd Markov-Prozess (DE-588)4134948-9 gnd
subject_GND	(DE-588)4121729-9 (DE-588)4274463-5 (DE-588)4012277-3 (DE-588)4126466-6 (DE-588)4134948-9
title	Multidimensional diffusion processes
title_auth	Multidimensional diffusion processes
title_exact_search	Multidimensional diffusion processes
title_full	Multidimensional diffusion processes Daniel W. Stroock ; S. R. Srinivasa Varadhan
title_fullStr	Multidimensional diffusion processes Daniel W. Stroock ; S. R. Srinivasa Varadhan
title_full_unstemmed	Multidimensional diffusion processes Daniel W. Stroock ; S. R. Srinivasa Varadhan
title_short	Multidimensional diffusion processes
title_sort	multidimensional diffusion processes
topic	Diffusion processes Stochastik (DE-588)4121729-9 gnd Diffusionsprozess (DE-588)4274463-5 gnd Diffusion (DE-588)4012277-3 gnd Martingal (DE-588)4126466-6 gnd Markov-Prozess (DE-588)4134948-9 gnd
topic_facet	Diffusion processes Stochastik Diffusionsprozess Diffusion Martingal Markov-Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007692407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000395
work_keys_str_mv	AT stroockdanielw multidimensionaldiffusionprocesses AT varadhansrs multidimensionaldiffusionprocesses

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