In this article, we establish new central limit theorems for Ruppert-Polyak averaged stochastic gradient descent schemes. Compared to previous work do not assume that convergence occurs an isolated attractor but instead allow a stable manifold. On the manifold target function is constant and oscillations of iterates in tangential direction may be significantly larger than ones normal direction....

We study the asymptotic behavior of stochastic hyperbolic–parabolic equations with slow–fast time scales. Both strong and weak convergence in averaging principle are established. Then we fluctuations original system around its averaged equation. show that normalized difference converges weakly to solution a linear wave An extra diffusion term appears limit which is given explicitly terms Poisso...

Motivated by the recent developments on iterate averaging of recursive stochastic approximation algorithms and asymptotic analysis of sign-error algorithms for adaptive filtering, this work develops two-stage sign algorithms for adaptive filtering. The proposed algorithms are based on constructions of a sequence of estimates using large step sizes followed by iterate averaging. Our main effort ...

The class of one-dimensional equations driven by a stochastic measure μ is studied. For only σ-additivity in probability assumed. This includes the Burgers equation and heat equation. existence uniqueness solution are proved, averaging principle for

A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quan...

The effect of internal noise for a mesoscopic chemical oscillator is studied analytically in a parameter region outside, but close to, the supercritical Hopf bifurcation. By normal form calculation and a stochastic averaging procedure, we obtain stochastic differential equations for the oscillation amplitude r and phase theta that is solvable. Noise-induced oscillation and internal noise cohere...