Randomness may exist in the initial value or in the differential operator or both. In [1,2], the authors discussed the general order conditions and a global convergence proof is given for stochastic Runge-Kutta methods applied to stochastic ordinary differential equations (SODEs) of Stratonovich type. In [3,4], the authors discussed the random Euler method and the conditions for the mean square...

In this paper we develop an L2-theory for stochastic partial differential equations driven by Lévy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of the coefficients is assumed.

This paper develops a new stability theory for stochastic functional differential systems with random switching. It examines general that are time inhomogeneous, past-dependent, and perturbed by Brownian motion modulated switching process. In contrast to the advances in literature, this provides weaker more verifiable conditions. Examples discussion also given demonstrate applicability of our r...