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Statistics and Control of Random Processes
Edited by: A. A. Novikov and A. N. Shiryaev
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Proceedings of the Steklov Institute of Mathematics
1995; 242 pp; softcover
Volume: 202
ISBN-10: 0-8218-0411-1
ISBN-13: 978-0-8218-0411-7
List Price: US$229 Member Price: US$183.20
Order Code: STEKLO/202

This book contains papers by participants in two seminars, one on Martingales and Statistics of Stochastic Processes, and one on Sequential Analysis, both of which are held at the Steklov Institute of the Russian Academy of Sciences. The papers develop the concepts of martingales and semimartingales and stochastic calculus for them, as well as their applications in statistics and control of stochastic processes. The class of semimartingales--that is, the class of all processes which can be represented as a sum of a martingale and a process with bounded variation--is rather large. It contains such important processes as Brownian motion, Poisson processes, solutions of stochastic differential equations, and others. The papers treat theoretical aspects of statistics of stochastic processes as well as specific models of stochastic processes from the standpoint of their statistics and control. The collection is intended for undergraduate and graduate students and resarchers in probability theory and mathematical statistics.

Readership

Undergraduates, graduates, and researchers in probability theory and mathematical statistics.

Table of Contents

• A. A. Afanas'ev -- On estimation of a parameter for systems with physical white noise
• A. E. Bashirov -- Linear filtering under dependent white and wide-band noises
• A. A. Butov -- Some random environments statistical problems for observable birth-and-death processes
• A. Yu. Veretennikov -- On large deviations in the averaging principle for stochastic difference equations on a torus
• A. A. Gushchin -- On the convergence of sequences of semimartingales and their components
• V. M. Dochviri -- Optimal stopping of a nonterminating homogeneous standard Markov process on a finite time interval
• V. P. Dragalin -- Optimality of generalized CUSUM procedure in quickest detection problem
• V. V. Konev and S. M. Pergamenshchikov -- Guaranteed estimation of autoregression parameters on the basis of a sequential correlational method
• N. V. Krylov -- On a proof of Itô's formula
• R. Sh. Liptser -- The Bogolyubov averaging principle for semimartingales
• M. B. Malyutov, V. G. Spokoĭnyĭ, and L. A. H. Uaraka -- On asymptotic properties of estimates under sequential design
• A. A. Novikov and B. A. Èrgashev -- Limit theorems for the first passage time of autoregression process over a level
• I. V. Pavlov -- Lower bound for the expected size of a learning sample for sequential pattern recognition procedures
• A. E. Rodkina -- On solvability and averaging for stochastic functional-differential equations with respect to a semimartingale
• V. G. Spokoĭnyĭ -- On construction of optimal strategies of parameter estimation for controllable systems
• A. N. Shiryaev and V. G. Spokoĭnyĭ -- On the concept of $$\lambda$$-convergence of statistical experiments
• A. G. Tartakovskiĭ -- Asymptotically minimax multialternative sequential rule for disorder detection
• M. Hitsuda -- Canonical representation of a Gaussian semimartingale and the innovation
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