Abstract To model subsurface flow in uncertain heterogeneous or fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient—also called random field—may be used. In case of one-dimensional parameter space, Lévy processes allow for jumps and display great flexibility the distributions However, various situations (e.g. microstructure modeling), space is not sufficie...

This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

where (0 l ) is the ensemble-averaging operation. The higher order moments can be determined by forming the ensemble average of different combinations of u(x, t) with the help of (1.4). Unfortunately, the Green’s function, G(x, t ; x’, t’), of (l.l), (1.2) and (1.3) cannot be obtained in terms of elementary or special functions except for the simplest cases. In general, we will have to obtain G...

this paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable hilbert space. themain technique is based upon an appropriate composition theorem combined with the banachcontraction mapping principle and an analytic semigroup of linear operators.

In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.