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AuthorSilvestrov, Dmitrii S. author
TitleLimit Theorems for Randomly Stopped Stochastic Processes [electronic resource] / by Dmitrii S. Silvestrov
ImprintLondon : Springer London : Imprint: Springer, 2004
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Descript XIV, 398 p. online resource


Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area is that of limit theorems for randomly stopped stochastic processes. This volume is the first to present a state-of-the-art overview of this field, with many of the results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast, and technically demanding, Russian literature in detail. A survey of the literature and an extended bibliography of works in the area are also provided. The coverage is thorough, streamlined and arranged according to difficulty for use as an upper-level text if required. It is an essential reference for theoretical and applied researchers in the fields of probability and statistics that will contribute to the continuing extensive studies in the area and remain relevant for years to come


1 Weak convergence of stochastic processes -- 1.1 Introductory remarks -- 1.2 Weak convergence in Rm -- 1.3 Weak convergence in metric spaces -- 1.4 The space D of cร dlร g functions -- 1.5 J-continuous functionals -- 1.6 J-convergence of cร dlร g processes -- 2 Weak convergence of randomly stopped stochastic processes -- 2.1 Introductory remarks -- 2.2 Randomly stopped scalar cร dlร g processes -- 2.3 Randomly stopped vector cร dlร g processes -- 2.4 Weakened continuity conditions -- 2.5 Iterated weak limits -- 2.6 Scalar compositions of cร dlร g processes -- 2.7 Vector compositions of cร dlร g processes -- 2.8 Translation theorems -- 2.9 Randomly stopped locally compact cร dlร g processes -- 3 J-convergence of compositions of stochastic processes -- 3.1 Introductory remarks -- 3.2 Compositions with asymptotically continuous components -- 3.3 Asymptotically continuous external processes -- 3.4 Asymptotically continuous internal stopping processes -- 3.5 Semi-vector compositions of cร dlร g functions -- 3.6 Semi-vector compositions of cร dlร g processes -- 3.7 Vector compositions of cร dlร g functions -- 3.8 Vector compositions of cร dlร g processes -- 4 Summary of applications -- 4.1 Introductory remarks -- 4.2 Randomly stopped sum-processes -- 4.3 Generalised exceeding processes -- 4.4 Step generalised exceeding processes -- 4.5 Sum-processes with renewal stopping -- 4.6 Accumulation processes -- 4.7 Extremes with random sample size -- 4.8 Mixed sum-max processes -- 4.9 Max-processes with renewal stopping -- 4.10 Shock processes -- Bibliographical remarks -- References

Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes


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