| Stochastic Processes: Lectures Given at Aarhus University 2004 Edition Contributor(s): Ito, Kiyosi (Author), Barndorff-Nielsen, Ole E. (Editor), Sato, Ken-Iti (Editor) |
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ISBN: 3540204822 ISBN-13: 9783540204824 Publisher: Springer OUR PRICE: $80.74 Product Type: Hardcover - Other Formats Published: March 2004 Annotation: This is a readily accessible introduction to the theory of stochastic processes with emphasis on processes with independent increments and Markov processes. After preliminaries on infinitely divisible distributions and martingales, Chapter 1 gives a thorough treatment of the decomposition of paths of processes with independent increments, today called the L??vy-It?? decomposition, in a form close to It??'s original paper from 1942. Chapter 2 contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. Two separate Sections present about 70 exercises and their complete solutions. The text and exercises are carefully edited and footnoted, while retaining the style of the original lecture notes from Aarhus University. |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General |
| Dewey: 519.23 |
| LCCN: 2004044984 |
| Physical Information: 0.76" H x 6.51" W x 9.33" (1.08 lbs) 236 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The volume Stochastic Processes by K. It 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 L vy-It decomposition of additive processes. Encouraged by Professor It 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. L vy'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 L vy-It decomposition. This is thoroughly treated, as- suming no continuity property in time, in a form close to the original 1942 paper of It , which gave rigorous expression to L vy's intuitive understanding of path behavior. |