概要Overview

This year we celebrate 120th anniversary of Andrey Kolmogorov, the founder of the modern theory of probability and stochastic processes. In the first part of the talk, we consider the contribution made by Kolmogorov to stochastic analysis. In particular, we will present some results related to the extension of Kolmogorov’s maximal inequality for random walks to the case of continuous and discontinuous martingales. Besides, we will also consider the case of some mean-reverting processes with a jump component. In the second part of the talk, we will demonstrate some results (obtained using martingale technique) on explicit calculations of characteristics of some first passages times and other related functionals used in sequential analysis for testing and estimation of parameters of mean-reverting processes.

This presentation is based on recent papers jointly with Dr. Nino Kordzakhia (Macquarie University, Sydney) and Albert Shiryaev (Steklov Mathematical Institute).

講師ご略歴Profile for speakers

Alexander Novikov is the Emeritus Professor at the Department of Mathematical Sciences, University of Technology Sydney.

Prior to this, since 1970 he was a Leading Research Fellow at the Steklov Mathematical Institute. Alexander lives in Australia since 1996. His research interest includes stochastic processes, statistics of random processes, sequential analysis, random fields, and mathematical finance.

He received a Ph.D. in Mathematics in 1972 and his Doctor of Science degree in 1982, both from the Steklov Mathematical Institute.

Alexander is the author of Novikov’s Condition (see https://en.wikipedia.org/wiki/Novikov%27s_condition).

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