Continuous Strong Markov Processes in Dimension One
Assing, Sigurd.
Continuous Strong Markov Processes in Dimension One A stochastic calculus approach / [electronic resource] : by Sigurd Assing, Wolfgang M. Schmidt. - XII, 140 p. online resource. - Lecture Notes in Mathematics, 1688 0075-8434 ; . - Lecture Notes in Mathematics, 1688 .
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.
9783540697862
10.1007/BFb0096151 doi
Distribution (Probability theory.
Mathematical statistics.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
QA273.A1-274.9 QA274-274.9
519.2
Continuous Strong Markov Processes in Dimension One A stochastic calculus approach / [electronic resource] : by Sigurd Assing, Wolfgang M. Schmidt. - XII, 140 p. online resource. - Lecture Notes in Mathematics, 1688 0075-8434 ; . - Lecture Notes in Mathematics, 1688 .
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.
9783540697862
10.1007/BFb0096151 doi
Distribution (Probability theory.
Mathematical statistics.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
QA273.A1-274.9 QA274-274.9
519.2