Our first result is a stochastic sewing lemma with quantitative estimates for mild incremental processes, which we study SPDEs driven by fractional Brownian motions in random environment. We obtain uniform [Formula: see text]-bounds. second averaging principle admitting non-stationary fast environments. As an application, prove SPDEs.

The stochastic optimal control is an important research subject in structural engineering. Recently, a stochastic optimal nonlinear control method has been proposed based on the stochastic dynamical programming principle and stochastic averaging method. The active and semi-active stochastic optimal control methods have been further developed for structural systems. The control saturation or bou...

Bayesian predictions are stochastic just like predictions of any other inference scheme that generalize from a nite sample. While a simple variational argument shows that Bayes averaging is generalization optimal given that the prior matches the teacher parameter distribution the situation is less clear if the teacher distribution is unknown. I deene a class of averaging procedures, the tempera...

We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-path analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and sufficient noise conditions for convergence of the ave...