arXiv subjects

Elena Chernousova

Publications and source records attributed to Elena Chernousova.

6 recordsLinked to original sources

arXiv2021

Lecture Notes on Stochastic Processes

This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied Mathematics and Informatics at Moscow Institute of Physics and Technology. The base of this course was formed and taught for decades by professors from the Department of Mathematical Foundations of Control A.A. Natan, S.A. Guz, and O.G. Gorbachev. Besides standard chapters of stochastic processes theory (correlation theory, Markov processes) in this book (and lectures) the following chapters are included: von Neumann-Birkhoff-Khinchin ergodic theorem, macrosystem equilibrium concept, Markov Chain Monte Carlo, Markov decision processes and the secretary problem.

math.PR↗

arXiv2018

Steady states of lattice population models with immigration

We consider the time evolution of the lattice subcritical Galton-Watson model with immigration. We prove Carleman type estimation for the cumulants in the simple case (binary splitting) and show the existence of a steady state. We also present the formula of the limiting distribution in a particular solvable case.

math.PR↗

arXiv2018

Steady state for the subcritical contact branching random walk on the lattice with the arbitrary number of offspring and with immigration

We consider the subcritical contact branching random walk on Zd in continuous time with the arbitrary number of offspring and with immigration. We prove the existence of the steady state (statistical equilibrium).

math.PR↗

arXiv2017

Strongly convex stochastic online optimization on a unit simplex with application to the mixing least square regression

In this paper we propose a new approach to obtain mixing least square regression estimate by means of stochastic online mirror descent in non-euclidian set-up.

math.OC↗

arXiv2017

Stochastic Analysis in Problems, part 1 (in Russian)

This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer Science. Range of the given exercises covers most of the significant classical results of the area including techniques that arise in modern stochastic disciplines. The book is recommended for the course "Stochastic Analysis in problems" which is held by the Department of Mathematical Foundations of Control in Moscow Institute of Physics and Technology. Content of the book may be used for practical classes, exams and for self-education reasons in various stochastic disciplines.

math.PR↗

arXiv2012

Ordered Smoothers With Exponential Weighting

The main goal in this paper is to propose a new method for deriving oracle inequalities related to the exponential weighting method. For the sake of simplicity we focus on recovering an unknown vector from noisy data with the help of a family of ordered smoothers. The estimators withing this family are aggregated using the exponential weighting and the aim is to control the risk of the aggregated estimate. Based on simple probabilistic properties of the unbiased risk estimate, we derive new oracle inequalities and show that the exponential weighting permits to improve Kneip's oracle inequality.

math.ST↗