Limit Theorems for Stochastic Processes

Produktbeschreibung

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. The second
edition contains some additions to the text and references. Some parts
are completely rewritten. 

Inhaltsverzeichnis

From the contents:
- The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals
- Characteristics of Semimartingales and Processes with Independent Increments
- Martingale Problems and Changes of Measures
- Hellinger Processes, Absolute Continuity and Singularity of Measures
- Contiguity, Entire Separation, Convergence in Variation
- Skorokhod Topology and Convergence of Processes
- Convergence of Processes with Independent Increments
- Convergence to a Process with Independent Increments
- Convergence to a Semimartingale
- Limit Theorems, Density Processes and Contiguity
- Bibliographical Comments
- References
- Index of Symbols
- Index of Terminology
- Index of Topics
- Index of Conditions for Limit Theorems