Author | Silvestrov, Dmitrii S. author |
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Title | Limit Theorems for Randomly Stopped Stochastic Processes [electronic resource] / by Dmitrii S. Silvestrov |
Imprint | London : Springer London : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-85729-390-9 |
Descript | XIV, 398 p. online resource |
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