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Limit Theorems for Randomly Stopped Stochastic Processes: Probability and Its Applications

Autor Dmitrii S. Silvestrov
en Limba Engleză Paperback – 23 oct 2012
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 andremain relevant for years to come.
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Specificații

ISBN-13: 9781447110514
ISBN-10: 144711051X
Pagini: 416
Ilustrații: XIV, 398 p.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.58 kg
Ediția:Softcover reprint of the original 1st ed. 2004
Editura: SPRINGER LONDON
Colecția Springer
Seria Probability and Its Applications

Locul publicării:London, United Kingdom

Public țintă

Research

Cuprins

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 càdlàg functions.- 1.5 J-continuous functionals.- 1.6 J-convergence of càdlàg processes.- 2 Weak convergence of randomly stopped stochastic processes.- 2.1 Introductory remarks.- 2.2 Randomly stopped scalar càdlàg processes.- 2.3 Randomly stopped vector càdlàg processes.- 2.4 Weakened continuity conditions.- 2.5 Iterated weak limits.- 2.6 Scalar compositions of càdlàg processes.- 2.7 Vector compositions of càdlàg processes.- 2.8 Translation theorems.- 2.9 Randomly stopped locally compact càdlàg 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 càdlàg functions.- 3.6 Semi-vector compositions of càdlàg processes.- 3.7 Vector compositions of càdlàg functions.- 3.8 Vector compositions of càdlàg 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.

Caracteristici

First book to provide a state-of-the-art overview of both the theory and the applications Covers and demystifies the vast, and technically demanding, Russian literature in detail Coverage is thorough, streamlined and arranged according to difficulty to aid use as an upper level text

Descriere

Descriere de la o altă ediție sau format:
This volume is the first to present a state-of-the-art overview of this field, with many 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. Its coverage is thorough, streamlined and arranged according to difficulty.