Investigations in the Theory of Stochastic Processes

ISBN-13: 9781468481594 / Angielski / Miękka / 2012 / 98 str.

V. N. Sudakov

Opis

This volume contains eight artieles by five authors. The common theme is indicated by the title, "Investigations in the Theory of Stochastic Processes. " The artiele by Vershik and Sudakov is a summary of severallectures delivered by the authors on the general aspects of measure theory in linear spaces. The main attention here is focused on the development of certain general concepts within whose framework are studied both the foundations of the theory of random processes as weIl as more specialized probIems. The published summary does not presume prior acquaintance with the subj eet. The group of artieles by Ibragimov and Solev is devoted to questions connected with the regular- ity of stationary random processes. Ibragimov, in "Conditions for the Complete Regularity of Station- ary Processes with Continuous Time," derives suffiient conditions for the complete regularity of a stationary random process with continuous time. The case of a rapid decrease of the regularity coef- ficient (in power or exponential form) is investigated. In his other artiele, "Complete Regularity of Generalized Stationary Random Processes," he shows that the problem of investigating the conditions for the complete regularity of generalized stationary random processes reduces to the analogous problem for general stationary random processes.

Spis treści

Probability Measures in Infinite-Dimensional Spaces.- Conditions for the Complete Regularity of Continuous-Time Stationary Processes.- Complete Regularity of Generalized Stationary Processes.- A Condition for the Regularity of a Stationary Gaussian Sequence.- A Condition for the Linear Regularity of a Stationary Vector-Valued Sequence.- Asymptotic Behavior of the Prediction Error in the Multidimensional Case.- Measures Defined by Markov Times.- Characterization of Random Functions by Random Preimages.