Estimate on the pathwise Lyapunov exponent of linear stochastic differential equations with constant coefficients. (English) Zbl 1197.93160
Summary: In this article, we study the problem of estimating the pathwise Lyapunov exponent for linear stochastic systems with multiplicative noise and constant coefficients. We present a Lyapunov type matrix inequality that is closely related to this problem, and show under what conditions we can solve the matrix inequality. From this we can deduce an upper bound for the Lyapunov exponent. In the converse direction, it is shown that a necessary condition for the stochastic system to be pathwise asymptotically stable can be formulated in terms of controllability properties of the matrices involved.
MSC:
| 93E15 | Stochastic stability in control theory |
| 15A24 | Matrix equations and identities |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
linear stochastic differential equations; Lyapunov exponent; matrix inequalities; stabilityReferences:
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