Continuous Strong Markov Processes in Dimension One: A Stochastic Calculus Approach - Lecture Notes in Mathematics 1688 | Probability Theory Textbook for Graduate Students & Researchers | Applied in Financial Modeling & Physics Research

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.