Ebook: Limit Theorems for Stochastic Processes

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.

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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.

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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.
Content:
Front Matter....Pages I-XX
The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals....Pages 1-63
Characteristics of Semimartingales and Processes with Independent Increments....Pages 64-141
Martingale Problems and Changes of Measures....Pages 142-226
Hellinger Processes, Absolute Continuity and Singularity of Measures....Pages 227-283
Contiguity, Entire Separation, Convergence in Variation....Pages 284-323
Skorokhod Topology and Convergence of Processes....Pages 324-388
Convergence of Processes with Independent Increments....Pages 389-455
Convergence to a Process with Independent Increments....Pages 456-520
Convergence to a Semimartingale....Pages 521-591
Limit Theorems, Density Processes and Contiguity....Pages 592-628
Back Matter....Pages 629-664

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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.
Content:
Front Matter....Pages I-XX
The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals....Pages 1-63
Characteristics of Semimartingales and Processes with Independent Increments....Pages 64-141
Martingale Problems and Changes of Measures....Pages 142-226
Hellinger Processes, Absolute Continuity and Singularity of Measures....Pages 227-283
Contiguity, Entire Separation, Convergence in Variation....Pages 284-323
Skorokhod Topology and Convergence of Processes....Pages 324-388
Convergence of Processes with Independent Increments....Pages 389-455
Convergence to a Process with Independent Increments....Pages 456-520
Convergence to a Semimartingale....Pages 521-591
Limit Theorems, Density Processes and Contiguity....Pages 592-628
Back Matter....Pages 629-664
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