Limit Theorems for Randomly Stopped Stochastic Processes
2004 (English)Book (Other academic)
The book is devoted to studies of weak limit theorems for randomly stopped stochastic processes and functional limit theorems for compositions of stochastic processes. A survey of basic results related to weak convergence of random variables and stochastic processes, including basic facts concerning the convergence of càdlàg processes in topologies J and U is given. General conditions of weak convergence for randomly stopped stochastic processes and compositions of càdlàg processes are presented. Functional limit theorems about convergence of compositions of càdlàg processes in topologies U and J are given. Applications to random sums, extremes with random sample size, generalised exceeding processes, sum-processes with renewal stopping, accumulation processes, max-processes with renewal stopping, and shock processes are presented. The book also contains an extended bibliography of works in the area.
Place, publisher, year, edition, pages
London: Springer , 2004. , XIV + 398 p.
, Probability and its Applications
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:su:diva-45706ISBN: 1-85233-777-XOAI: oai:DiVA.org:su-45706DiVA: diva2:369396