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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 998–1004 (Mi semr1110)

Probability theory and mathematical statistics

On the distribution of the trajectory maximum of a random walk with switchings

V. I. Lotovab

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: We continue studying of the random walk introduced in [1]. The distribution of the random walk jumps changes under successive achievement regulatory boundaries. The regulation is intended to keep under control the range of trajectories. At the same time the structure of the process allows the trajectories stay some time outside the band adjustments. The paper establishes limit theorems for the distribution of the maximum possible excess of the upper regulatory barrier.

Keywords: oscillating random walk, trajectory maximum, limit theorems.

 Funding Agency Grant Number Russian Science Foundation 18-11-00129

DOI: https://doi.org/10.33048/semi.2019.16.068

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Bibliographic databases:

UDC: 519.21
MSC: 60G50
Received April 24, 2019, published August 5, 2019

Citation: V. I. Lotov, “On the distribution of the trajectory maximum of a random walk with switchings”, Sib. Èlektron. Mat. Izv., 16 (2019), 998–1004

Citation in format AMSBIB
\Bibitem{Lot19} \by V.~I.~Lotov \paper On the distribution of the trajectory maximum of a random walk with switchings \jour Sib. \Elektron. Mat. Izv. \yr 2019 \vol 16 \pages 998--1004 \mathnet{http://mi.mathnet.ru/semr1110} \crossref{https://doi.org/10.33048/semi.2019.16.068} `