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| 2. |
- Silvestrov, D.S.
(author)
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Exponential asymptotics for a perturbed renewal equation
- 1996
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In: Theory of Probability and Mathematical Statistics. - 0094-9000. ; :52, s. 153-162
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Journal article (peer-reviewed)abstract
- Exponential asymptotic expansions of a new type are obtained for solutions of perturbed renewal equations. Some important ergodic theorems and limit theorems on the convergence in law of stopping time functionals for regenerative processes are generalized for mixed versions of these theorems. These theorems applied to stopping times cover both theorems on the convergence of distributions and large-deviation-type theorems
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| 3. |
- Silvestrov, D.S.
(author)
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Limit theorems for randomly stopped stochastic processes
- 2006
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In: Journal of Mathematical Sciences. - : Springer Science and Business Media LLC. - 1072-3374 .- 1573-8795. ; 138:1, s. 5467-5471
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Journal article (peer-reviewed)abstract
- General conditions of weak and J-convergence for superposition of stochastic processes are formulated
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| 4. |
- Silvestrov, D:S.
(author)
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Limit Theorems for Randomly Stopped Stochastic Processes
- 2004
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Book (other academic/artistic)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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