Stochastic evolution equations with respect to semimartingales in hilbert space

Abstract

We consider the stochastic evolution equation on a Hilbert space H written formally as dX_t= A(t)X_t dt + dZ(X)_t t∈[0,T], where {A(t),∈[Q,T]} is a family of infinitesimal generations of Co-semigroups on H and Z(X) is a semimartingale with values in H which may depend on the process X. We define several types of solutions of this equation, under the assumption that ∩∈[o,T]D(*(t))is dense in H. The main purpose of this paper is to investigate relationships among these solutions

Keywords:

• Lyapunov exponent
• ergodic stationary systems
• multiplicative ergodic theorem

* Research partially supported by a CONACyT student scholarship and by Prof. L. G. Gorostiza's CONACyT grant PCEXCNA-040319.

* Research partially supported by a CONACyT student scholarship and by Prof. L. G. Gorostiza's CONACyT grant PCEXCNA-040319.

Notes

* Research partially supported by a CONACyT student scholarship and by Prof. L. G. Gorostiza's CONACyT grant PCEXCNA-040319.