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

Jan Haškovec

Applications of Mathematics (2022)

  • Volume: 67, Issue: 4, page 471-483
  • ISSN: 0862-7940

Abstract

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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).

How to cite

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Haškovec, Jan. "Asymptotic and exponential decay in mean square for delay geometric Brownian motion." Applications of Mathematics 67.4 (2022): 471-483. <http://eudml.org/doc/298301>.

@article{Haškovec2022,
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).},
author = {Haškovec, Jan},
journal = {Applications of Mathematics},
keywords = {geometric Brownian motion; delay; asymptotic decay; exponential decay},
language = {eng},
number = {4},
pages = {471-483},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic and exponential decay in mean square for delay geometric Brownian motion},
url = {http://eudml.org/doc/298301},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Haškovec, Jan
TI - Asymptotic and exponential decay in mean square for delay geometric Brownian motion
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 471
EP - 483
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).
LA - eng
KW - geometric Brownian motion; delay; asymptotic decay; exponential decay
UR - http://eudml.org/doc/298301
ER -

References

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