Mimicking the one-dimensional marginal distributions of processes having an ito differential

Abstract

Let ξ(t) be a stochastic process starting from 0 with Ito differential {Mathematical expression} where {Mathematical expression} is a Wiener process, δ and β are bounded {Mathematical expression} processes such that δδT is uniformly positive definite. Then it is proved that there exists a stochastic differential equation {Mathematical expression} with non-random coefficients which admits a weak solution x(t) having the same one-dimensional probability distribution as ξ(t) for every t. The coefficients σ and b have a simple interpretation: {Mathematical expression} © 1986 Springer-Verlag.