The book presents an indepth study of arbitrary onedimensional continuous strong Markov processes using methods of shastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary nonregular 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 shastic differential equations and fundamental examples of irregular diffusions.
The book presents an indepth study of arbitrary onedimensional continuous strong Markov processes using methods of shastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary nonregular 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 shastic differential equations and fundamental examples of irregular diffusions.
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