Geodesic
Asymptotic and exponential decay in mean square for delay geometric Brownian motion
Applications of Mathematics, Tome 67 (2022) no. 4, pp. 471-483 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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).
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).
DOI : 10.21136/AM.2021.0358-20
Classification : 34K11, 34K25, 34K50, 60H10
Keywords: geometric Brownian motion; delay; asymptotic decay; exponential decay 
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     author = {Ha\v{s}kovec, Jan},
     title = {Asymptotic and exponential decay in mean square for delay geometric {Brownian} motion},
     journal = {Applications of Mathematics},
     pages = {471--483},
     year = {2022},
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Haškovec, Jan. Asymptotic and exponential decay in mean square for delay geometric Brownian motion. Applications of Mathematics, Tome 67 (2022) no. 4, pp. 471-483. doi: 10.21136/AM.2021.0358-20

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