On approximation of solutions to a class of stochastic equations (Q5932627)

The article is devoted to studying the problem of approximation of solutions to stochastic equations in \(\theta\)-integrals which generalize the Itô and Stratonovich stochastic integrals. The authors prove that if the smoothing of a Brownian motion is represented as a linear combination of Itô and Stratonovich smoothings, then a solution to stochastic equations in \(\theta\)-integrals for \(0\leq\theta\leq 1/2\) can be approximated by a solution to the average finite-difference equation in the space \(L^2(\Omega, {\mathcal A}, P)\) over random variables and uniformly with respect to nonrandom variables. The authors also discuss the case of \(1/2 < \theta \leq 1\) and, incidentally, obtain estimates for the rate of convergence.