Yurachkovskij, A. P. Weak convergence of recurrent sequences to processes of diffusion type. (English. Russian original) Zbl 0659.60085 Theory Probab. Math. Stat. 35, 109-120 (1987); translation from Teor. Veroyatn. Mat. Stat. 35, 96-105 (1986). The author states sufficient conditions for the weak convergence to weak solutions of an Itô equation with functional coefficients of step processes built using stochastic finite differences. In the case of Markovian coefficients, he proves that the conditions are also necessary. MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60B10 Convergence of probability measures Keywords:weak convergence; weak solutions of an Itô equation PDFBibTeX XMLCite \textit{A. P. Yurachkovskij}, Theory Probab. Math. Stat. 35, 109--120 (1987; Zbl 0659.60085); translation from Teor. Veroyatn. Mat. Stat. 35, 96--105 (1986)