Root / CYBERNETICS AND PHYSICS / Volume 15, 2026, Number 2 / On almost sure asymptotic stability of linear stochastic systems with multiplicative disturbances and random coefficients

On almost sure asymptotic stability of linear stochastic systems with multiplicative disturbances and random coefficients

Ekaterina Palamarchuk

This paper considers the behavior of solutions to systems of linear stochastic differential equations with multiplicative disturbances and random coefficients. We present conditions for almost sure exponential stability in terms of integrated-time averages of logarithmic matrix norms. The study also analyzes instability conditions. To complete the analysis, we investigate the pathwise asymptotic boundedness and unboundedness of solutions. We then illustrate this approach by applying it to a two-dimensional cooperative-competitive system with sine-Wiener noise perturbations.
CYBERNETICS AND PHYSICS, VOL. 15, NO. 2, 2026, 206–215
https://doi.org/10.35470/2226-4116-2026-15-2-206-215

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