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- Silvestrov, D:S.
(författare)
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Limit Theorems for Randomly Stopped Stochastic Processes
- 2004
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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