Continuous Strong Markov Processes in Dimension One A stochastic cal
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 diffusio
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1688
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1688
Springer
Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Sigurd Assing Wolfgang M. Schmidt
Continuous Strong Markov Processes in Dimension One A Stochastic Calculus Approach
Springer
Authors Sigurd Assing Universitat Bielefeld Fakultat fur Mathematik Postfach 100131 D-33501 Bielefeld
Wolfgang M. Schmidt Deutsche Bank AG OTC-Derivate GroBe GaliusstraBe 10-14 D- 60272 Frankfurt
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme Assing, Sigurd: Continuous strong Markov processes in dimension one : a stochastic calculus approach I Sigurd Assing ; Wolfgang Schmidt. - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo : Springer, 1998 (Lecture notes in mathematics; 1688) ISBN 3-540-64465-2
Mathematics Subject Classification (1991): 60125, 60G44, 60H20 ISSN 0075-8434 ISBN 3-540-64465-2 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Printed in Germany
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the authors SPIN: 10649856 46/3143-543210 - Printed on acid-free paper
To our sons Edgar, Gregor and Sebastian
Preface
The purpose of this book is the investigation of one-dimensional continuous strong Markov processes using methods of stochastic calculus. Markov processes are characterized by the principle of independence of future and past given the present value of the process, which goes back to A.A. MARKOV. The class of Markov processes plays an outstanding role in applications of random processes since many time dependent random phenomena can suitably be modelled by them. On the other hand, due to its manifold connections to other fields of mathematics, as for instance functional analysis, potential theory and partial differential equations, the theory of Markov processes is one of the most interesting branches of the theory of random processes. There are two basic approaches to the investigation of Markov processes. The analytical approach, which goes back in substan
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