Statistics and Control of Stochastic Processes

This volume contains papers presented at the Steklov Seminar on Statistics and Control of Stochastic Processes. For the past three decades, the seminar has determined the development, in a number of important directions, of the theory of random processes not only in the USSR (now Russia) but in the whole world. It was organised by A N Shiryaev in collaboration with N V Krylov and R Sh Liptser. It started off with optimal stopping and filtering with applications to engineering, and very soon extended its interests to more general problems of stochastic control, causal and anticipating stochastic calculus, limit theorems for semimartingales, martingale methods in queueing theory, foundations of statistics of random processes and, in recent years, mathematical finance. Many studies, for example of stochastic PDEs or extended stochastic integrals, anticipated largely Western works.

The contributions in this book are devoted to the hottest topics and united by a martingale methodology which was the key idea of the seminar.

Sample Chapter(s)
Moderate Deviations for Iterates of Expanding Maps (323 KB)

• Robert Liptser (Yu M Kabanov et al.)
• The Branching Diffusion Approximation for a Model of a Synchronized Queueing Network (N G Duffield et al.)
• The Turnpike Property and the Central Limit Theorem in Stochastic Models of Economic Dynamics (I V Evstigneev & S Flåm)
• A Stochastic Control Model for Hedging in Incomplete Markets (S Frasson & W J Runggaldier)
• On Sequential Estimation of Parameters in Continuous-Time Stochastic Regression (L Galtchouk & V Konev)
• Asymptotic Properties of an Approximation Maximum Likelihood Estimator for Stochastic PDEs (M Huebner et al.)
• On the Pontryagin Maximum Principle for SDEs with a Poisson-Type Driving Noise (Yu M Kabanov)
• On the FTAP of Kreps–Delbaen–Schachermayer (Yu M Kabanov)
• An Estimation of a Multivariate Density and Its Derivatives by Weakly Dependent Observations (G Koshkin & V Vasil'iev)
• Large Deviations for Non Diffusion Process (R Liptser)
• and other papers