Lévy processes and infinitely divisible distributions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Edition: | Corr. paperback ed., rev. ed. |
| Series: | Cambridge studies in advanced mathematics
68 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 521 S. |
| ISBN: | 9781107656499 1107656494 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Titel: Lévy processes and infinitely divisible distributions
Autor: Sato, Ken-iti
Jahr: 2013
Contents
Preface to the revised edition ix
Preface to the first printing xi
Remarks on notation xiii
Chapter 1. Basic examples 1
1. Definition of Levy processes 1
2. Characteristic functions 7
3. Poisson processes 14
4. Compound Poisson processes 18
5. Brownian motion 21
6. Exercises 1 28
Notes 29
Chapter 2. Characterization and existence
of Levy and additive processes 31
7. Infinitely divisible distributions and Levy processes in law 31
8. Representation of infinitely divisible distributions 37
9. Additive processes in law 47
10. Transition functions and the Markov property 54
11. Existence of Levy and additive processes 59
12. Exercises 2 66
Notes 68
Chapter 3. Stable processes and their extensions 69
13. Selfsimilar and semi-selfsimilar processes and their exponents 69
14. Representations of stable and semi-stable distributions 77
15. Selfdecomposable and semi-selfdecomposable distributions 90
16. Selfsimilar and semi-selfsimilar additive processes 99
17. Another view of selfdecomposable distributions 104
18. Exercises 3 114
Notes 116
Chapter 4. The Levy-Ito decomposition of sample functions 119
19. Formulation of the Levy-Ito decomposition 119
20. Proof of the Levy-Ito decomposition 125
V
vi CONTENTS
21. Applications to sample function properties 135
22. Exercises 4 142
Notes 144
Chapter 5. Distributional properties of Levy processes 145
23. Time dependent distributional properties 145
24. Supports 148
25. Moments 159
26. Levy measures with bounded supports 168
27. Continuity properties 114
28. Smoothness 189
29. Exercises 5 193
Notes 196
Chapter 6. Subordination and density transformation 197
30. Subordination of Levy processes 191
31. Infinitesimal generators of Levy processes 205
32. Subordination of semigroups of operators 212
33. Density transformation of Levy processes 217
34. Exercises 6 233
Notes 236
Chapter 7. Recurrence and transience 237
35. Dichotomy of recurrence and transience 237
36. Laws of large numbers 245
37. Criteria and examples 250
38. The symmetric one-dimensional case 263
39. Exercises 7 270
Notes 272
Chapter 8. Potential theory for Levy processes 273
40. The strong Markov property 273
41. Potential operators 281
42. Capacity 295
43. Hitting probability and regularity of a point 313
44. Exercises 8 328
Notes 331
Chapter 9. Wiener-Hopf factorizations 833
45. Factorization identities 333
46. Levy processes without positive jumps 345
47. Short time behavior 351
48. Long time behavior 363
49. Further factorization identities 369
50. Exercises 9 382
CONTENTS vii
Notes 383
Chapter 10. More distributional properties 385
51. Infinite divisibility on the half line 385
52. Unimodality and strong unimodality 394
53. Selfdecomposable processes 403
54. Unimodality and multimodality in Levy processes 416
55. Exercises 10 424
Notes 426
Supplement 427
56. Forms of Levy-Khintchine representation 427
57. Independently scattered random measures 430
58. Relations of representations of selfdecomposable distributions 435
59. Remarkable classes of infinitely divisible distributions 436
60. Lebesgue decomposition for path space measures 439
61. Supports of Levy processes 446
62. Densities of multivariate stable distributions 447
63. Conditions stronger than subexponentiality 450
64. Class of c-decomposable distributions 453
Solutions to exercises 457
References and author index 481
Subject index
513
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| spelling | Sato, Ken-iti 1934- Verfasser (DE-588)142290580 aut Kahō-katei Lévy processes and infinitely divisible distributions Ken-Iti Sato Corr. paperback ed., rev. ed. Cambridge [u.a.] Cambridge Univ. Press 2013 XIV, 521 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 68 Unbeschränkt teilbare Verteilung (DE-588)4788273-6 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Lévy-Prozess (DE-588)4463623-4 s Unbeschränkt teilbare Verteilung (DE-588)4788273-6 s DE-604 Cambridge studies in advanced mathematics 68 (DE-604)BV000003678 68 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027276728&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 |
| spellingShingle | Sato, Ken-iti 1934- Lévy processes and infinitely divisible distributions Cambridge studies in advanced mathematics Unbeschränkt teilbare Verteilung (DE-588)4788273-6 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| subject_GND | (DE-588)4788273-6 (DE-588)4463623-4 (DE-588)4113937-9 |
| title | Lévy processes and infinitely divisible distributions |
| title_alt | Kahō-katei |
| title_auth | Lévy processes and infinitely divisible distributions |
| title_exact_search | Lévy processes and infinitely divisible distributions |
| title_full | Lévy processes and infinitely divisible distributions Ken-Iti Sato |
| title_fullStr | Lévy processes and infinitely divisible distributions Ken-Iti Sato |
| title_full_unstemmed | Lévy processes and infinitely divisible distributions Ken-Iti Sato |
| title_short | Lévy processes and infinitely divisible distributions |
| title_sort | levy processes and infinitely divisible distributions |
| topic | Unbeschränkt teilbare Verteilung (DE-588)4788273-6 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| topic_facet | Unbeschränkt teilbare Verteilung Lévy-Prozess Hochschulschrift |
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