Nonnormality and Stochastic Differential Equations∗
نویسندگان
چکیده
A highly nonnormal Jacobian may give rise to large transients. This behaviour has been shown to have implications for (a) the relevance of linearising a nonlinear system and (b) the timestep restrictions required to keep a numerical method stable. Here, we show that nonnormality also manifests itself for stochastic differential equations. We give an example of a family of systems that is stable without noise, but can be made exponentially unstable in mean-square by a noise perturbation that shrinks to zero as the nonnormality increases. We then show via finite-time convergence theory that an Euler approximation shares the same property, giving a discrete analogue of the result.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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تاریخ انتشار 2005