02698nam a22003375i 4500978-1-4757-1776-1cr nn 008mamaa130402s1982 xxu: s :::: 0:eng d9781475717761ENGUSQA274-274.9519.2Online resource: SpringerChung, Kai Lai.1917-2009.Lectures from Markov Processes to Brownian Motion[EBook]by Kai Lai Chung.New York, NYSpringer1982.VIII, 242 pages : 5 illus.online resource.textonline resourceGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,0072-7830 ;2491 Markov Process -- 2 Basic Properties -- 3 Hunt Process -- 4 Brownian Motion -- 5 Potential Developments.This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book as the Course, and may be considered as a general background; its specific use is limited to the mate rial on discrete parameter martingale theory cited in § 1. 4. Apart from this and some dispensable references to Markov chains as examples, the book is self-contained.Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)Markov processesProbabilities.Brownian motion processesProbability Theory and Stochastic Processes.SpringerLink (Online service)Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,249http://dx.doi.org/10.1007/978-1-4757-1776-1