Stochastic Processes: Lectures Given at Aarhus University - Couverture rigide

Ito, Kiyosi; Barndorff-Nielsen, O. E.

Couverture rigide

ISBN 10 : 3540204822 ISBN 13 : 9783540204824

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2004

Synopsis

This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.

A propos du livre

À propos de la quatrième de couverture

The volume Stochastic Processes by K. Itö was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968­ 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the Lévy-It ö decomposition of additive processes. Encouraged by Professor It ó we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ran­ dom variables are treated using the dispersion as a main tooI. Lévy's form of characteristic functions of infinitely divisible distributions and basic proper­ ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure the­ orem describes the decomposition of sample functions of additive processes, known today as the Lévy-Itó decomposition. This is thoroughly treated, as­ suming no continuity property in time, in a form close to the original 1942 paper of Itó, which gave rigorous expression to Lévy's intuitive understanding of path behavior.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 2004
• Langue: anglais
• ISBN 10: 3540204822
• ISBN 13: 9783540204824
• Reliure: Relié
• Nombre de pages: 236
• Éditeur: Sato Kenichi
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne