Continuous Strong Markov Processes in Dimension One : A Stochastic Calculus Approach. 1st ed. 1998

種類:

電子ブック

責任表示:

by Sigurd Assing, Wolfgang M. Schmidt

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998

著者名:

• Assing, Sigurd.
• Schmidt, Wolfgang M.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1688

ISBN:

9783540697862 [3540697861]    

注記:

Basic concepts and preparatory results -- Classification of the points of the state space -- Weakly additive functionals and time change of strong Markov processes -- Semimartingale decomposition of continuous strong Markov semimartingales -- Occupation time formula -- Construction of continuous strong Markov processes -- Continuous strong Markov semimartingales as solutions of stochastic differential equations.
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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