Asymptotic and exponential decay in mean square for delay geometric Brownian motion

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 resol...

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Bibliographic Details
Published in:Applications of mathematics (Prague) 2022-08, Vol.67 (4), p.471-483
Main Author: Haškovec, Jan
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Asymptotic methods
Asymptotic properties
Brownian motion
Classical and Continuum Physics
Decay
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimization
Theoretical
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Summary: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 a forward-backward estimate for the square mean (exponential decay).
ISSN:0862-7940
1572-9109
DOI:10.21136/AM.2021.0358-20