Martingales and stochastic integrals
著者
書誌事項
Martingales and stochastic integrals
Cambridge University Press, 2008
- : pbk
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注記
Originally published: 1984
"Digitally printed version 2008"--T.p. verso
"Paperback Re-issue"--Back cover
"Text has grown out of graduate lecture courses given at the University of Hull"--Pref.
Bibliography: p. 194-197
Includes index
内容説明・目次
内容説明
This book provides an introduction to the rapidly expanding theory of stochastic integration and martingales. The treatment is close to that developed by the French school of probabilists, but is more elementary than other texts. The presentation is abstract, but largely self-contained and Dr Kopp makes fewer demands on the reader's background in probability theory than is usual. He gives a fairly full discussion of the measure theory and functional analysis needed for martingale theory, and describes the role of Brownian motion and the Poisson process as paradigm examples in the construction of abstract stochastic integrals. An appendix provides the reader with a glimpse of very recent developments in non-commutative integration theory which are of considerable importance in quantum mechanics. Thus equipped, the reader will have the necessary background to understand research in stochastic analysis. As a textbook, this account will be ideally suited to beginning graduate students in probability theory, and indeed it has evolved from such courses given at Hull University. It should also be of interest to pure mathematicians looking for a careful, yet concise introduction to martingale theory, and to physicists, engineers and economists who are finding that applications to their disciplines are becoming increasingly important.
目次
- Preface
- Probabilistic background
- 1. Weak compactness and uniform integrability
- 2. Discrete time martingales
- 3. Continuous-time martingales
- 4. Stochastic integrals
- Appendix
- References
- List of symbols
- Index.
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