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Stability of High-Order Linear Itô Equations with Delays
Department of Mathematics, Vancouver Island University, Nanaimo, Canada
Dagestan Research Center of the Russian Academy of Sciences & Department of Mathematics, Dagestan State University, Makhachkala, Russia
Faculty of Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
- 1 Department of Mathematics, Vancouver Island University, Nanaimo, Canada
- 2 Dagestan Research Center of the Russian Academy of Sciences & Department of Mathematics, Dagestan State University, Makhachkala, Russia
- 3 Faculty of Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
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Abstract
A novel general stability analysis scheme based on a non-Lyapunov framework is explored. Several easy-to-check sufficient conditions for exponential p -stability are formulated in terms of M -matrices. Stability analysis of applied second-order Itô equations with delay is provided as well. The linearization technique, in combination with the tests obtained in this paper, can be used for local stability analysis of a wide class of nonlinear stochastic differential equations.
KeywordsHigh-Order Stochastic ModelsDelayStabilityNon-Lyapunov Methods<em>M</em>-Matrices
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