The averaging principle for BSDEs and one-barrier RBSDEs, with Lipschitz coefficients, is investigated. An averaged the original proposed, as well their solutions are quantitatively compared. Under some appropriate assumptions, to systems can be approximated by stochastic in sense of mean square.

The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation in a setting with innovations satisfying some averaging properties and to study some applications. The averaging assumptions allow us to unify the framework where the innovations are generated (to solve problems from Numerical Probability) and the one with exogenous innovations (market data...

We explore the relationship between weighted averaging and stochastic approxima tion algorithms and study their convergence via a sample path analysis We prove that the convergence of a stochastic approximation algorithm is equivalent to the con vergence of the weighted average of the associated noise sequence We also present necessary and su cient noise conditions for convergence of the averag...

Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging ([22, 36]), we present stochastic block dual averaging (SBDA)—a novel class of block subgradient methods for convex nonsmooth and stochastic optimization. SBDA re...