A. I. Sakhanenko

Sobolev Institute of Mathematics

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Yu. Yu. Linke

Sobolev Institute of Mathematics

Vitali Wachtel

Bielefeld University

Denis Denisov

University of Manchester

Qianqian Zhou

Guangdong University of Technology

АА

А. А. Боровков

Sobolev Institute of Mathematics

Junyi Guo

Amazon (United States)

A. D. Shelepova

Raúl Montes-de-Oca

Universidad Autónoma Metropolitana

Junyi Guo

Nankai University

Francisco Salem-Silva

Universidad Veracruzana

Cooperative Institutions

Novosibirsk State University

Sobolev Institute of Mathematics

Nankai University

Russian Academy of Sciences

University of Augsburg

Novosibirsk Tuberculosis Research Institute

Siberian Branch of the Russian Academy of Sciences

University of Manchester

Ludwig-Maximilians-Universität München

Nanjing University of Posts and Telecommunications

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Asymptotically optimal estimation in a linear regression problem with random errors in coefficients

Siberian Mathematical Journal (2010)

Yu. Yu. Linke A. I. Sakhanenko

Asymptotically optimal algorithm

Errors-in-Variables Models

10.1007/s11202-010-0012-9

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Citations (4)

Estimates for perturbations of general discounted Markov control chains

Applicationes Mathematicae (2003)

Raúl Montes-de-Oca A. I. Sakhanenko Francisco Salem-Silva

We extend previous results of the same authors ([11]) on the effects of perturbation in the transition probability of a Markov cost chain for discounted Markov control processes. Supposing valid, for each stationary policy, conditions of Lyapunov and Harr

Markov kernel

Markov renewal process

10.4064/am30-3-4

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Citations (8)

First-passage times for random walks with non-identically distributed increments

arXiv (Cornell University) (2016)

Denis Denisov A. I. Sakhanenko Vitali Wachtel

We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time $n$ converges, as $n\to\infty$, towards the Brownian meander.

Meander (mathematics)

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On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process

Sibirskie Elektronnye Matematicheskie Izvestiya (2021)

A. I. Sakhanenko Vitali Wachtel E. I. Prokopenko A. D. Shelepova

We consider a compound renewal process, which is also known as a cumulative renewal process, or a continuous time random walk.We suppose that the jump size has zero mean and nite variance, whereas the renewal-time has a moment of order greater than 3/2.We investigate the asymptotic behaviour of the probability that this process is staying above a moving non-increasing boundary up to time T which tends to innity.Our main result is a generalization of a similar one for ordinary random walks obtained earlier by Denisov D., Sakhanenko A. and

Renewal theory

10.33048/semi.2021.18.002

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Citations (1)

Crossing an Asymptotically Square-Root Boundary by the Brownian Motion

Proceedings of the Steklov Institute of Mathematics (2022)

Denis Denisov Günter Hinrichs A. I. Sakhanenko Vitali Wachtel

Square root

Square (algebra)

Reflected Brownian motion

Root (linguistics)

10.1134/s0081543822010096

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Citations (2)

Random walks with square-root boundaries: the case of exact boundaries $g(t)=c\sqrt{t+b}-a$

arXiv (Cornell University) (2025)

Denis Denisov A. I. Sakhanenko Sara Terveer Vitali Wachtel

Let $S(n)$ be a real valued random walk with i.i.d. increments which have zero mean and finite variance. We are interested in the asymptotic properties of the stopping time $T(g):=\inf\{n\ge1: S(n)\le g(n)\}$, where $g(t)$ is a boundary function. In the present paper we deal with the parametric family of boundaries $\{g_{a,b}(t)=c\sqrt{t+b}-a, b\ge0, a>c\sqrt{b}\}$. First, assuming that sufficiently many moments of increments of the walk are finite, we construct a positive space-time harmonic function $W(a,b)$. Then we show that there exist $p(c)>0$ and a constant $\varkappa(c)$ such that $\mathbf{P}(T_{g_{a,b}}>n)\sim \varkappa(c)\frac{W(a,b)}{n^{p(c)/2}}$ as $n\to\infty$.

Square root

Root (linguistics)

Square (algebra)

10.48550/arxiv.2501.04554

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Exponential bounds of ruin probabilities for non-homogeneous risk models

Probability and Mathematical Statistics (2020)

Qianqian Zhou A. I. Sakhanenko Junyi Guo

Lundberg-type inequalities for ruin probabilities of nonhomogeneous risk models are presented.By employing the martingale method, upper bounds of ruin probabilities are obtained for general risk models under weak assumptions.In addition, several risk models, including the newly defined united risk model and a quasi-periodic risk model with interest rate, are studied.

Ruin theory

10.37190/0208-4147.41.2.2

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Invariance principle for the sum of minima

Siberian Mathematical Journal (1986)

Yu. I. Gladysheva A. I. Sakhanenko

Maxima and minima

Invariance principle

10.1007/bf00969026

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Citations (3)