Continuous Strong Markov Processes in Dimension One [electronic resource] : A stochastic calculus approach / by Sigurd Assing, Wolfgang M. Schmidt.
Material type: TextSeries: Lecture Notes in Mathematics ; 1688Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998Description: XII, 140 p. online resourceContent type:- text
- computer
- online resource
- 9783540697862
- 519.2 23
- QA273.A1-274.9
- QA274-274.9
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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