Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorGut, Allan. author
TitleStopped Random Walks [electronic resource] : Limit Theorems and Applications / by Allan Gut
ImprintNew York, NY : Springer New York : Imprint: Springer, 1988
Connect tohttp://dx.doi.org/10.1007/978-1-4757-1992-5
Descript IX, 199 p. online resource

SUMMARY

My first encounter with renewal theory and its extensions was in 1967/68 when I took a course in probability theory and stochastic processes, where the then recent book Stochastic Processes by Professor N.D. Prabhu was one of the requirements. Later, my teacher, Professor Carl-Gustav Esseen, gave me some problems in this area for a possible thesis, the result of which was Gut (1974a). Over the years I have, on and off, continued research in this field. During this time it has become clear that many limit theorems can be obtained with the aid of limit theorems for random walks indexed by families of positive, integer valued random variables, typically by families of stopping times. During the spring semester of 1984 Professor Prabhu visited Uppsala and very soon got me started on a book focusing on this aspect. I wish to thank him for getting me into this project, for his advice and suggestions, as well as his kindness and hospitality during my stay at Cornell in the spring of 1985. Throughout the writing of this book I have had immense help and support from Svante Janson. He has not only read, but scrutinized, every word and every formula of this and earlier versions of the manuscript. My gratitude to him for all the errors he found, for his perspicacious suggestions and remarks and, above all, for what his unusual personal as well as scientific generosity has meant to me cannot be expressed in words


CONTENT

I Limit Theorems for Stopped Random Walks -- II Renewal Processes and Random Walks -- III Renewal Theory for Random Walks with Positive Drift -- IV Generalizations and Extensions -- V Functional Limit Theorems -- Appendix A. Some Facts from Probability Theory -- 1 Convergence of Moments. Uniform Integrability -- 2 Moment Inequalities for Martingales -- 3 Convergence of Probability Measures -- 4 Strong Invariance Principles -- 5 Problems -- Appendix B. Some Facts about Regularly Varying Functions -- 1 Introduction and Definitions -- 2 Some Results


Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram