Applications of Mathematics, Vol. 67, No. 4, pp. 471-483, 2022

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

Jan Haškovec

Received December 14, 2020.   Published online September 3, 2021.

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 a forward-backward estimate for the square mean (exponential decay).
Keywords:  geometric Brownian motion; delay; asymptotic decay; exponential decay
Classification MSC:  34K11, 34K25, 34K50, 60H10

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Affiliations:   Jan Haškovec, King Abdullah University of Science and Technology, 23955-6900 Thuwal, Kingdom of Saudi Arabia, e-mail:

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