Multiplicative ergodic theorem for discontinuous cocycles

Details Multiplicative ergodic theorem for discontinuous cocycles Multiplicative ergodic theorem for discontinuous cocycles

2012-04-23

arxiv.org/abs/1204.5050v1

Mathematics

Probability

23 pages

Scientific paper

Motivated by studying stochastic systems with non-Gaussian L\'evy noise, spectral properties for linear discontinuous 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 a linear stochastic system with general L\'evy motions. Finally, Lyapunov exponents are considered for linear stochastic differential equations with $\alpha$-stable L\'evy motions.

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