Algebraic computation of the statistics of the solution of some nonlinear stochastic differential equations

This paper presents an algebraic method for computing the statistics of the solution of some stochastic non-linear differential equations by mean of the Volterra functional expansion. The symbolic calculus introduced, based on noncommutative variables and iterated integrals has the advantage of allowing easily the use of symbolic computation systems, like REDUCE or MACSYMA, to perform the manipulations. This becomes necessary as soon as one tries to get high order terms.