Continuous strong Markov processes in dimension one : a stochastic calculus approach

Sigurd Assing, Wolfgang M. Schmidt

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

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[目次]

  • Basic concepts and preparatory results
  • classification of the points of the state space
  • weakly additive functionals and time change of strong Markov processes
  • semi-martingale decomposition of continuous strong Markov semi-martingales
  • occupation time formula
  • construction of continuous strong Markov processes
  • continuous strong Markov semi-martingales as solutions of stochastic differential equations.

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この本の情報

書名 Continuous strong Markov processes in dimension one : a stochastic calculus approach
著作者等 Assing, Sigurd
Schmidt, Wolfgang M.
Schmidt W.
Assing A.
シリーズ名 Lecture notes in mathematics
出版元 Springer
刊行年月 c1998
ページ数 xii, 135 p.
大きさ 24 cm
ISBN 3540644652
NCID BA36020524
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言語 英語
出版国 ドイツ
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