Regularity theory for a new class of fractional parabolic stochastic evolution equations

A new class of fractional-order parabolic stochastic evolution equations of the form (∂t+A)γX(t)=W˙Q(t) , t∈ [0 , T] , γ∈ (0 , ∞) , is introduced, where - A generates a C -semigroup on a separable Hilbert space H and the spatiotemporal driving noise W˙ ^Q is the formal time derivative of an H-valued cylindrical Q-Wiener process....

Hydrodynamics for the partial exclusion process in random environment

In this paper, we introduce a random environment for the exclusion process in Z^d obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we...

Stochastic Evolution Equations with Adapted Drift

In this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance mathematical finance and filtration theory. Second,...

Non-autonomous stochastic Cauchy problems in Banach spaces