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.
Author(s): Sigurd Assing, Wolfgang M. Schmidt (auth.)
Series: Lecture Notes in Mathematics 1688
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1998
Language: English
Pages: 140
Tags: Probability Theory and Stochastic Processes; Statistical Theory and Methods
Basic concepts and preparatory results....Pages 1-13
Classification of the points of the state space....Pages 15-25
Weakly additive functionals and time change of strong Markov processes....Pages 27-32
Semimartingale decomposition of continuous strong Markov semimartingales....Pages 33-52
Occupation time formula....Pages 53-77
Construction of continuous strong Markov processes....Pages 79-102
Continuous strong Markov semimartingales as solutions of stochastic differential equations....Pages 103-118
