Numerical solution of random differential equations: A mean square approach

This paper deals with the construction of numerical solutions of random initial value differential problems by means of a random Euler difference scheme whose mean square convergence is proved based on conditions expressed in terms of the mean square behavior of the right-hand side of the underlying random differential equation. A random mean value theorem is required and established. The concept of mean square modulus of continuity is also introduced and illustrative examples and possibilities are included. Expectation and variance of the approximating process are computed.