We prove maximal L-regularity for the stochastic evolution equation

Let V →֒ H →֒ V ∗ be a normal triple of spaces with dense and continuous embeddings, where V is a reflexive Banach space, H is a Hilbert space, identified with its dual by means of the inner product in H , and V ∗ is the dual of V . Let W = (Wt)t≥0 be an r-dimensional Brownian motion carried by a stochastic basis (Ω,F , (Ft)t≥0, P ). In this paper, we study the approximation of the solution to th...

In this paper, we show two new results on the existence and uniqueness of solution Neutral Stochastic Pantograph Integro-Differential Equations (NSPIDE) exponential stability in mean square using one-sided Growth Condition. One example is exhibited to interest our results.

A characterisation of the quantum stochastic bounded generators of irreversible quantum state evolutions is given. This suggests the general form of quantum stochastic evolution equation with respect to the Poisson (jumps), Wiener (diffusion) or general Quantum Noise. The corresponding irreversible Heisenberg evolution in terms of stochastic completely positive (CP) cocycles is also characteriz...