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  3. Martingales and Stochastic Integrals
  • Cited by 46
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    • Publisher:
      Cambridge University Press
      Publication date:
      07 October 2011
      13 September 1984
      ISBN:
      9780511897221
      9780521090339
      DOI:
      https://doi.org/10.1017/CBO9780511897221
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.32kg, 216 Pages
      • Subjects:
      Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Probability Theory and Stochastic Processes, Statistics and Probability
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    • Selected: Digital
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    Subjects:
    Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Probability Theory and Stochastic Processes, Statistics and Probability
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    Book description

    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.

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