Items related to Limit Theorems for Randomly Stopped Stochastic Processes
Synopsis
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 cądląg functions.- 1.5 J-continuous functionals.- 1.6 J-convergence of cądląg processes.- 2 Weak convergence of randomly stopped stochastic processes.- 2.1 Introductory remarks.- 2.2 Randomly stopped scalar cądląg processes.- 2.3 Randomly stopped vector cądląg processes.- 2.4 Weakened continuity conditions.- 2.5 Iterated weak limits.- 2.6 Scalar compositions of cądląg processes.- 2.7 Vector compositions of cądląg processes.- 2.8 Translation theorems.- 2.9 Randomly stopped locally compact cądląg 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 cądląg functions.- 3.6 Semi-vector compositions of cądląg processes.- 3.7 Vector compositions of cądląg functions.- 3.8 Vector compositions of cądląg 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.
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