Continuous Strong Markov Processes in Dimension One

A Stochastic Calculus Approach

Sigurd Assing, Wolfgang M. Schmidt (Autoren)

Buch | Softcover

XII, 140 Seiten

1998
Springer Berlin (Verlag)
978-3-540-64465-1 (ISBN)

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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.

Erscheint lt. Verlag	20.5.1998
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 140 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	226 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Calculus • Markov process • Markov-Prozesse • Martingale • semimartingale • Stochastic Calculus
ISBN-10	3-540-64465-2 / 3540644652
ISBN-13	978-3-540-64465-1 / 9783540644651
Zustand	Neuware