Multidimensional diffusion processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1997
|
| Edition: | Corr. 2. print. |
| Series: | Die Grundlehren der mathematischen Wissenschaften
233 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 338 S. graph. Darst. |
| ISBN: | 0387903534 3540903534 |
Staff View
MARC
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Record in the Search Index
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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
|
| any_adam_object | 1 |
| author | Stroock, Daniel W. 1940- Varadhan, S. R. S. 1940- |
| author_GND | (DE-588)130519561 (DE-588)13051957X |
| author_facet | Stroock, Daniel W. 1940- Varadhan, S. R. S. 1940- |
| author_role | aut aut |
| author_sort | Stroock, Daniel W. 1940- |
| author_variant | d w s dw dws s r s v srs srsv |
| building | Verbundindex |
| bvnumber | BV011438109 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.75 |
| callnumber-search | QA274.75 |
| callnumber-sort | QA 3274.75 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)35029577 (DE-599)BVBBV011438109 |
| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
| dewey-sort | 3519.2 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 2. print. |
| format | Book |
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| id | DE-604.BV011438109 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:09:46Z |
| institution | BVB |
| isbn | 0387903534 3540903534 |
| language | English |
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| 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 |
| spelling | Stroock, Daniel W. 1940- Verfasser (DE-588)130519561 aut Multidimensional diffusion processes Daniel W. Stroock ; S. R. Srinivasa Varadhan Corr. 2. print. Berlin u.a. Springer 1997 XII, 338 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften 233 Diffusion processes Stochastik (DE-588)4121729-9 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Diffusion (DE-588)4012277-3 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Diffusion (DE-588)4012277-3 s Diffusionsprozess (DE-588)4274463-5 s 1\p DE-604 Stochastik (DE-588)4121729-9 s 2\p DE-604 Martingal (DE-588)4126466-6 s 3\p DE-604 Varadhan, S. R. S. 1940- Verfasser (DE-588)13051957X aut Die Grundlehren der mathematischen Wissenschaften 233 (DE-604)BV000000395 233 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |