Random Walk in Random and Non-random EnvironmentsWorld Scientific, 2005 - 396 pages The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results OCo mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk. Since the first edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved problems and conjectures which have since been settled; this second revised and enlarged edition includes those new results. Three new chapters have been added: frequently and rarely visited points, heavy points and long excursions. This new edition presents the most complete study of, and the most elementary way to study, the path properties of the Brownian motion." |
Autres éditions - Tout afficher
Random Walk in Random and Non-random Environments Pál Révész,Pal Revesz Aucun aperçu disponible - 1990 |
Expressions et termes fréquents
2n log log Annals of Probability Assume behaviour Borel-Cantelli lemma Brownian motion C₁ Clearly consequence of Theorem Csáki define disc EFKP LIL Erdős excursions fact finitely Földes formulate Hence increments independent inequality integer interval Invariance Principle iterated logarithm law of large lg lg LIL of Khinchine lim inf lim sup limit distribution limit points limit theorem log n log log n)2 log nk log₂ log3 logn longest M+(n Math min{k n₁ n₂ nk+1 notations obtain THEOREM P{p₁ P{Sn P{X₁ p₁ positive constant positive integer positive numbers probability space proof of Theorem properties proved THEOREM random environment random walk rate of convergence Recurrence Theorem Remark resp result Révész Section sequence of positive Similarly Strassen's theorem stronger Theorem trivial consequence visited Wiener process