Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2001
|
| Series: | Lecture notes in mathematics
1766 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 144 S. |
| ISBN: | 3540424156 |
Staff View
MARC
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
I. General facts about the method, purpose of the paper 1
1. Limit theorems for Markov chains 1
2. Stochastic properties of dynamical systems 2
3. Historical background to the method 3
4. Purpose of the paper 4
II. The central limit theorems for Markov chains 6
1. The concept of quasi compact operator 6
2. Conditions fl[m] and V, notations J f 8
3. Statements of the central limit theorems 11
III. Quasi compact operators of diagonal type and perturbations 14
1. Definition, properties 14
2. A perturbation theorem 18
IV. First properties of Fourier kernels, application 23
1. Properties of the Fourier kernels 23
2. Central limit theorem : intermediate result 27
V. Peripheral eigenvalues of Fourier kernels 31
1. Eigenvalues of Q(t) of modulus 1 31
2. Peripheral eigenvalues of Q(t) for small t 34
VI. Proofs of Theorems A, B, C 38
1. Conditions ti m . Central limit theorem (Theorem A) 38
2. Development of the characteristic function 38
3. Central limit theorem with a rate of convergence (Theorem B) 39
4. Local central limit theorem (Theorem C) 41
VII. Renewal theorem for Markov chains (Theorem D) 43
1. Statements 43
2. Proof of Theorem VII.2 44
VIII. Large deviations for Markov chains (Theorem E) 49
1. Statement of the main result 49
2. Properties of the Laplace kernels, function c 50
3. Logarithmic estimate : Theorem E (i) (ii) 52
4. Probability of a large deviation : Theorem E (iii) 54
5. Additional statements 58
IX. Ergodic properties for Markov chains 60
X. Markov chains associated with Lipschitz kernels 63
1. General facts, contraction properties 63
2. Invariant distributions and quasi compactness 64
3. Laplace kernels 70
4. Products of invertible random matrices 75
5. Products of positive random matrices 78
6. Autoregresive processes 79
XI. Stochastic properties of dynamical systems 81
1. Statements 81
2. r invariant distribution, relativized Markov kernel 84
3. Proofs of the limit theorems 86
XII. Expanding maps 89
1. Piecewise expanding maps of the interval 89
2. Subshifts and transfer operators 93
XIII. Proofs of some statements in Probability Theory 99
1. Example of a two state Markov chain 99
2. Proof of Lemma IV 5 101
3. Large deviations lemma 102
XIV. Functional analysis results on quasi compactness 104
1. A sufficient condition for quasi compactness 104
2. Proof of the perturbation theorem (Theorem III.8) HI
Generalization to the non ergodic case, by L. Herve 115
References 141
Indexes 145
|
| any_adam_object | 1 |
| author | Hennion, Hubert Hervé, Loïc |
| author_facet | Hennion, Hubert Hervé, Loïc |
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| id | DE-604.BV013865834 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:25Z |
| institution | BVB |
| isbn | 3540424156 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009484537 |
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| physical | 144 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Hennion, Hubert Verfasser aut Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness Hubert Hennion ; Loïc Hervé Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2001 144 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1766 Dynamisches System - Stochastischer Prozess Markov-Kette - Grenzwertsatz Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s Grenzwertsatz (DE-588)4158163-5 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Dynamisches System (DE-588)4013396-5 s Hervé, Loïc Verfasser aut Lecture notes in mathematics 1766 (DE-604)BV000676446 1766 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009484537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hennion, Hubert Hervé, Loïc Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness Lecture notes in mathematics Dynamisches System - Stochastischer Prozess Markov-Kette - Grenzwertsatz Grenzwertsatz (DE-588)4158163-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Dynamisches System (DE-588)4013396-5 gnd Markov-Kette (DE-588)4037612-6 gnd |
| subject_GND | (DE-588)4158163-5 (DE-588)4057630-9 (DE-588)4013396-5 (DE-588)4037612-6 |
| title | Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness |
| title_auth | Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness |
| title_exact_search | Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness |
| title_full | Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness Hubert Hennion ; Loïc Hervé |
| title_fullStr | Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness Hubert Hennion ; Loïc Hervé |
| title_full_unstemmed | Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness Hubert Hennion ; Loïc Hervé |
| title_short | Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness |
| title_sort | limit theorems for markov chains and stochastic properties of dynamical systems by quasi compactness |
| topic | Dynamisches System - Stochastischer Prozess Markov-Kette - Grenzwertsatz Grenzwertsatz (DE-588)4158163-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Dynamisches System (DE-588)4013396-5 gnd Markov-Kette (DE-588)4037612-6 gnd |
| topic_facet | Dynamisches System - Stochastischer Prozess Markov-Kette - Grenzwertsatz Grenzwertsatz Stochastischer Prozess Dynamisches System Markov-Kette |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009484537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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