This paper is devoted to the non-asymptotic analysis of Ruppert–Polyak averaging method introduced in Polyak and Juditsky (1992) Ruppert (1988)[26] for minimization a smooth function f with stochastic algorithm. We first establish general optimal bound: if θˆn position algorithm at step n, we prove that E|θˆn−argmin(f)|2⩽Tr(Σ⋆)n+Cd,fn−rβ,where Σ⋆ limiting covariance matrix CLT demonstrated Cd,f...

In the problem of remote estimation by a centralized observer, improvements to accuracy observer estimates come at cost higher communication bandwidth and energy consumption. this article we improve reducing measurement variance on sensor node before its transmission node. The main contribution is show that trade-off between dynamical system variance. As result there an optimal averaging time m...

Transcription is often stochastic. This is seemingly incompatible with the importance of gene expression during development. Here we show that during zebrafish embryogenesis, transcription activation is stochastic due to (1) genes acquiring transcriptional competence at different times in different cells, (2) differences in cell cycle stage between cells, and (3) the stochastic nature of transc...

We study the validity of an averaging principle for a slow-fast system of stochastic reaction-diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging principle in terms of the invariant measure of the fast equation is no longer available. As an alternative, we introduce the time-dependent evolution family ...