TY - JOUR
T1 - Asymptotic and Exponential Decay in Mean Square for Delay Geometric Brownian Motion
AU - Haskovec, Jan
N1 - KAUST Repository Item: Exported on 2021-09-29
Acknowledgements: J. Haškovec acknowledges the support of the KAUST baseline funds.
PY - 2021/9/3
Y1 - 2021/9/3
N2 - 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).
AB - 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).
UR - http://hdl.handle.net/10754/663494
UR - http://articles.math.cas.cz/10.21136/AM.2021.0358-20
UR - http://www.scopus.com/inward/record.url?scp=85115339223&partnerID=8YFLogxK
U2 - 10.21136/AM.2021.0358-20
DO - 10.21136/AM.2021.0358-20
M3 - Article
SN - 1572-9109
SP - 1
EP - 13
JO - Applications of Mathematics
JF - Applications of Mathematics
ER -