Limit theorems for functionals of random walks:
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| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence ; Rhode Island
American Math. Society
1995
|
| Series: | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics
195 = 1995,2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russichen übersetzt |
| Physical Description: | viii, 259 Seiten |
| ISBN: | 0821804383 |
Staff View
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| 240 | 1 | 0 | |a Predel'nye teoremy dlja funkcionalov ot slučajnych bluždanij |
| 245 | 1 | 0 | |a Limit theorems for functionals of random walks |c by A. N. Borodin and I. A. Ibragimov ; Edited by V. N. Sudakov |
| 264 | 1 | |a Providence ; Rhode Island |b American Math. Society |c 1995 | |
| 300 | |a viii, 259 Seiten | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |v 195 = 1995,2 | |
| 500 | |a Aus dem Russichen übersetzt | ||
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| 700 | 1 | |a Sudaov, V. N. |4 edt | |
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Record in the Search Index
| _version_ | 1804124980910227456 |
|---|---|
| adam_text | CONTENTS
Introduction 1
Main Notation 5
CHAPTER I. Preliminary Facts 7
§1. Stable distributions. Convergence of distributions of sums of indepen¬
dent random variables to stable distributions 7
§2. Stable processes. Convergence to stable processes 10
§3. A characterization of a Brownian motion process with random time ... 14
§4. Local time of a stable process 18
CHAPTER II. Distributions of Functionals of Brownian Local Time 25
§ 1. Brownian local time 25
§2. Distributions of additive functionals of a Brownian motion process and
of the maximum and minimum functionals 26
§3. The Markov property 37
§4. Distributions of integral functionals of Brownian local time and func¬
tionals of supremum type 44
§5. The exact modulus of continuity of Brownian local time t(r. x) with
respect to the variable / 54
§6. The law of the iterated logarithm for Brownian local time 56
§7. Distribution of functionals of sojourn time type 58
§8. Distribution of the supremum of the increments of Brownian local time 67
§9. The exact modulus of continuity of Brownian local time i(t, x) with
respect to the variable x 72
CHAPTER III. Limit Theorems for Functionals of Normalized Sums 79
§ 1. Introduction 79
§2. Limit theorems for t]n . Limit theorems of the first type 84
§3. Limit theorems of the first type. Continuation 95
§4. Convergence of distributions of random processes ^Zk n, fn(Skn) 103
§5. Limit theorems of the second type 112
§6. Supplements and generalizations 121
CHAPTER IV. Limit Theorems for Additive and Multiadditive Functionals
of a Random Walk 131
§ 1. General limit theorems 131
§2. Limit theorems for integrable / 142
V
vi CONTENTS
§3. Limit theorems of the second type 146
§4. Random walks in the domain of attraction of the Cauchy law 150
§5. Random walks in E2 155
§6. Additive functional S /(5fc) determined by a periodic function / . 156
§7. The central limit theorem for Markov processes with normal transition
operator 164
§8. Strong form of the central limit theorem 169
§9. Applications to random walks on compact Abelian groups 171
CHAPTER V. Invariance Principle for Local Times 177
§1. Formulation of the problems 177
§2. Auxiliary results 179
§3. Weak invariance principle (integer random walks) 190
§4. Weak invariance principle (continuous random walks) 203
§5. On the nature of convergence to Brownian local time 212
§6. Strong invariance principle 228
§7. Applications of the invariance principle 238
Bibliographical Comments 249
Bibliography 255
|
| any_adam_object | 1 |
| author | Borodin, Andrej N. 1953- Ibragimov, Ilʹdar Abdullovič 1932- |
| author2 | Sudaov, V. N. |
| author2_role | edt |
| author2_variant | v n s vn vns |
| author_GND | (DE-588)12470218X (DE-588)172161991 |
| author_facet | Borodin, Andrej N. 1953- Ibragimov, Ilʹdar Abdullovič 1932- Sudaov, V. N. |
| author_role | aut aut |
| author_sort | Borodin, Andrej N. 1953- |
| author_variant | a n b an anb i a i ia iai |
| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 700 |
| ctrlnum | (OCoLC)33382297 (DE-599)BVBBV010514282 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T17:54:17Z |
| institution | BVB |
| isbn | 0821804383 |
| language | English Russian |
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| physical | viii, 259 Seiten |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | American Math. Society |
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| series | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| series2 | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| spelling | Borodin, Andrej N. 1953- (DE-588)12470218X aut Predel'nye teoremy dlja funkcionalov ot slučajnych bluždanij Limit theorems for functionals of random walks by A. N. Borodin and I. A. Ibragimov ; Edited by V. N. Sudakov Providence ; Rhode Island American Math. Society 1995 viii, 259 Seiten txt rdacontent n rdamedia nc rdacarrier Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 195 = 1995,2 Aus dem Russichen übersetzt Random walks (statistiek) gtt Limit theorems (Probability theory) Random walks (Mathematics) Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Grenzwertsatz (DE-588)4158163-5 s DE-604 Irrfahrtsproblem (DE-588)4162442-7 s 1\p DE-604 Ibragimov, Ilʹdar Abdullovič 1932- (DE-588)172161991 aut Sudaov, V. N. edt Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 195 = 1995,2 (DE-604)BV000009943 195 = 1995,2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007008059&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 | Borodin, Andrej N. 1953- Ibragimov, Ilʹdar Abdullovič 1932- Limit theorems for functionals of random walks Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics Random walks (statistiek) gtt Limit theorems (Probability theory) Random walks (Mathematics) Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| subject_GND | (DE-588)4162442-7 (DE-588)4057630-9 (DE-588)4158163-5 |
| title | Limit theorems for functionals of random walks |
| title_alt | Predel'nye teoremy dlja funkcionalov ot slučajnych bluždanij |
| title_auth | Limit theorems for functionals of random walks |
| title_exact_search | Limit theorems for functionals of random walks |
| title_full | Limit theorems for functionals of random walks by A. N. Borodin and I. A. Ibragimov ; Edited by V. N. Sudakov |
| title_fullStr | Limit theorems for functionals of random walks by A. N. Borodin and I. A. Ibragimov ; Edited by V. N. Sudakov |
| title_full_unstemmed | Limit theorems for functionals of random walks by A. N. Borodin and I. A. Ibragimov ; Edited by V. N. Sudakov |
| title_short | Limit theorems for functionals of random walks |
| title_sort | limit theorems for functionals of random walks |
| topic | Random walks (statistiek) gtt Limit theorems (Probability theory) Random walks (Mathematics) Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| topic_facet | Random walks (statistiek) Limit theorems (Probability theory) Random walks (Mathematics) Irrfahrtsproblem Stochastischer Prozess Grenzwertsatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007008059&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000009943 |
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