Asymptotic and exponential decay in mean square for delay geometric Brownian motion
Probability
2021-03-23 v2 Classical Analysis and ODEs
Dynamical Systems
Abstract
We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of asymptotic decay. For exponential decay, they are easily resolvable numerically. The analytical method is based on construction of a Lyapunov functional (asymptotic decay) and forward-backward estimate for the square mean (exponential decay).
Keywords
Cite
@article{arxiv.2005.03752,
title = {Asymptotic and exponential decay in mean square for delay geometric Brownian motion},
author = {Jan Haskovec},
journal= {arXiv preprint arXiv:2005.03752},
year = {2021}
}
Comments
10 pages, 2 figures