Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales.

Abstract: "We consider a class of stochastic linear functional differential systems driven by semimartingales with stationary ergodic increments. We allow smooth convolution-type dependence of the noise terms on the history of the state. Using a stochastic variational technique we construct a compactifying stochastic semiflow on the state space. A multiplicative Ruelle-Oseledec ergodic theorem then gives the existence of a discrete Lyapunov spectrum and a saddle-point property in the hyperbolic case."