Intersections of Random Walks:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1991
|
| Schriftenreihe: | Probability and Its Applications
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric |
| Beschreibung: | 1 Online-Ressource (IV, 220 p) |
| ISBN: | 9781475721379 9781475721393 |
| DOI: | 10.1007/978-1-4757-2137-9 |
Internformat
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Datensatz im Suchindex
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| author | Lawler, Gregory F. |
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| discipline | Mathematik |
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| spelling | Lawler, Gregory F. Verfasser aut Intersections of Random Walks by Gregory F. Lawler Boston, MA Birkhäuser Boston 1991 1 Online-Ressource (IV, 220 p) txt rdacontent c rdamedia cr rdacarrier Probability and Its Applications A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Arithmetisches Mittel (DE-588)4143009-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Irrfahrtsproblem (DE-588)4162442-7 s Arithmetisches Mittel (DE-588)4143009-8 s 2\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 3\p DE-604 https://doi.org/10.1007/978-1-4757-2137-9 Verlag Volltext 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 | Lawler, Gregory F. Intersections of Random Walks Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Arithmetisches Mittel (DE-588)4143009-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd |
| subject_GND | (DE-588)4143009-8 (DE-588)4057630-9 (DE-588)4162442-7 (DE-588)4143389-0 |
| title | Intersections of Random Walks |
| title_auth | Intersections of Random Walks |
| title_exact_search | Intersections of Random Walks |
| title_full | Intersections of Random Walks by Gregory F. Lawler |
| title_fullStr | Intersections of Random Walks by Gregory F. Lawler |
| title_full_unstemmed | Intersections of Random Walks by Gregory F. Lawler |
| title_short | Intersections of Random Walks |
| title_sort | intersections of random walks |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Arithmetisches Mittel (DE-588)4143009-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Arithmetisches Mittel Stochastischer Prozess Irrfahrtsproblem Aufgabensammlung |
| url | https://doi.org/10.1007/978-1-4757-2137-9 |
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