Classical and spatial stochastic processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | X, 178 S. graph. Darst. |
| ISBN: | 3764340819 0817640819 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface ix
I Discrete Time Markov Chains 1
1.1 Three fundamental examples 2
1.2 Classification of states 4
1.3 Finite Markov chains 11
1.4 Birth and death chains 13
1.5 An example of coupling 18
1.6 Time to get ruined 23
1.7 Absorption probabilities for martingales 25
1.8 Random walks 28
1.9 The Bienayme Galton Watson branching process 31
1.10 Proof of Theorem 1.2.1 35
1.11 Proof of Theorem 1.2.2 37
1.12 Proof of Theorem 1.9.1 38
II Stationary Distributions of a Markov Chain 43
II. 1 Existence of stationary distributions 44
11.2 Reversible measures 52
11.3 Convergence to a stationary distribution 57
11.4 The finite case 60
11.5 Proof of Proposition II. 1.2 64
11.6 Proof of Proposition II. 1.3 66
11.7 Proofs of Theorems II.3.1 and II.4.2 67
viii Contents
III Continuous Time Birth and Death Markov Chains 73
111.1 The exponential distribution 74
111.2 Construction and first properties 77
111.3 Limiting probabilities 83
111.4 Classification of states 89
111.5 The Poisson process 92
111.6 Passage times 97
111.7 A queue which is not Markovian 99
111.8 Proof of Theorem III.3.1 101
111.9 Proof of Theorem III.5.1 104
111.10 Proof of Theorem III.5.2 107
IV Percolation 111
IV.l Percolation on ld 112
IV.2 Further properties of percolation on Zd 116
IV.3 Percolation on a tree and two critical exponents 122
V A Cellular Automaton 127
V.I The model 127
V.2 A renormalization argument 130
VI Continuous Time Branching Random Walk 135
VI.1 A continuous time Bienayme Galton Watson process 136
VI.2 A continuous time branching random walk 137
VI.3 The first phase transition is continuous 143
VI.4 The second phase transition is discontinuous 145
VI.5 Proof of Theorem VI.2.1 148
VII The Contact Process on a Homogeneous Tree 153
VII. 1 The two phase transitions 154
VII.2 Characterization of the first phase transition 156
VII.3 The graphical construction 158
VII.4 Proofs 159
VII.5 Open problems 165
Appendix: Some Facts About Probabilities on Countable Spaces 167
1 Probability space 167
2 Independence 170
3 Discrete random variables 172
References 177
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:27:29Z |
| institution | BVB |
| isbn | 3764340819 0817640819 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008435692 |
| oclc_num | 245986596 |
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| spelling | Schinazi, Rinaldo B. 1958- Verfasser (DE-588)120793547 aut Classical and spatial stochastic processes Rinaldo B. Schinazi Boston ; Basel ; Berlin Birkhäuser 1999 X, 178 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Stochastischer Prozess Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schinazi, Rinaldo B. 1958- Classical and spatial stochastic processes Stochastischer Prozess Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Classical and spatial stochastic processes |
| title_auth | Classical and spatial stochastic processes |
| title_exact_search | Classical and spatial stochastic processes |
| title_full | Classical and spatial stochastic processes Rinaldo B. Schinazi |
| title_fullStr | Classical and spatial stochastic processes Rinaldo B. Schinazi |
| title_full_unstemmed | Classical and spatial stochastic processes Rinaldo B. Schinazi |
| title_short | Classical and spatial stochastic processes |
| title_sort | classical and spatial stochastic processes |
| topic | Stochastischer Prozess Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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