Abstract
We analyze the behavior of solutions of linear stochastic differential equations (SDEs) with time-varying coefficients. The underlying SDEs contain correlated additive and multiplicative disturbances as well as external input in the form of stochastic process. We obtain functions serving as upper bounds on solutions in the mean-square and almost sure sense as time increases. The results are used to study the subdiffusion modeling problem in which the velocity process is determined by the solution of a linear stochastic differential equation.
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This work was supported by the Russian Science Foundation, project no. 18-71-10097.
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Translated by V. Potapchouck
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Palamarchuk, E.S. On Asymptotic Behavior of Solutions of Linear Inhomogeneous Stochastic Differential Equations with Correlated Inputs. Diff Equat 58, 1291–1308 (2022). https://doi.org/10.1134/S00122661220100019
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DOI: https://doi.org/10.1134/S00122661220100019