Author	Assing, Sigurd. author
Title	Continuous Strong Markov Processes in Dimension One [electronic resource] : A stochastic calculus approach / by Sigurd Assing, Wolfgang M. Schmidt
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1998
Connect to	http://dx.doi.org/10.1007/BFb0096151
Descript	XII, 140 p. online resource

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

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

1. Mathematics
2. Probabilities
3. Statistics
4. Mathematics
5. Probability Theory and Stochastic Processes
6. Statistical Theory and Methods