A Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and Applications

Huijie Qiao, Jinqiao Duan

Published 2012-04-23, updated 2018-01-07Version 5

Motivated by studying stochastic systems with non-Gaussian L\'evy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem is proved for such linear cocycles. Then, the result is illustrated for two linear stochastic systems with general L\'evy motions.