On the estimation of backward stochastic differential equations

We consider an estimation problem for a backward stochastic differential equation in the presence of statistically uncertain noise. We use the approach of the theory of guaranteed estimation and assume that the statistically uncertain noise, as well as some processes entering the equation, is subject to integral constraints. In the linear case, we prove a theorem on the approximation of random information sets by deterministic sets as the diffusion coefficient vanishes. Examples are considered.