Limit Theorems for Stochastic Processes

Jean Jacod, Albert N. Shiryaev

680 pages, parution le 21/11/2002 (2^eme édition)

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Résumé

Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results.
The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.

Contents

Chapter I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals
Chapter II. Characteristics of Semimartingales and Processes with Independent Increments
Chapter III. Martingale Problems and Changes of Measures
Chapter IV. Hellinger Processes, Absolute Continuity and Singularity of Measures
Chapter V. Contiguity, Entire Separation, Convergence in Variation
Chapter VI. Skorokhod Topology and Convergence of Processes
Chapter VII. Convergence of Processes with Independent Increments
Chapter VIII. Convergence to a Process with Independent Increments
Chapter IX. Convergence to a Semimartingale
Chapter X. Limit Theorems, Density Processes and Contiguity

L'auteur - Jean Jacod

Universite de Paris VI, Paris, France;

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jean Jacod, Albert N. Shiryaev
Parution	21/11/2002
Édition	2^eme édition
Nb. de pages	680
Format	16 x 24
Couverture	Relié
Poids	1140g
Intérieur	Noir et Blanc
EAN13	9783540439325