Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Examples are sequential analysis, queueing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of counters. Stopped Random Walks: Limit Theorems and Applications shows how this theory can be used to prove limittheorems for renewal counting processes, first passage time processes, and certain two-dimenstional random walks, and to how these results are useful in various applications. This second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter examines nonlinear renewal processes in order to present the analagous theory for perturbed random walks, modeled as a random walk plus ‘noise’. Second edition featuresa new chapter on perturbed random walks, which are modeled as random walks plus ‘noise’ Presents updates to the first edition, including an outlook on further results, extensions, and generalizations on the subject Close to 100 additional bibliographic references added to some 200 original ones Concise blend of material useful for both the researcher and student of probability theory INDICE: Preface.- Notations and Symbols.- Introduction.- Limit Theorems for Stopped Random Walks.- Renewal Processes and Random Walks.- Renewal Theory for Random Walks with Positive Drift.- Generalizations and Extensions.- Functional Limit Theorems.- Perturbed Random Walks.- Appendix A: Some Facts from Probability Theory.- Appendix B: Some Facts about Regularly Varying Functions.- Bibliography.- Index.
- ISBN: 978-0-387-87834-8
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 270
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés