4 papers · 1 filter
Uniform-in-time Gaussian fluctuations for multiscale nonlinear stochastic systems via Malliavin Calculus
Shivam Singh Dhama
We establish a uniform-in-time quantitative central limit theorem (QCLT) for a nonlinear slow-fast stochastic system. We identify significant weaker sufficient conditions that enab…
Quantitative Fluctuation Analysis for Continuous-Time Stochastic Gradient Descent via Malliavin Calculus
Solesne Bourguin, Shivam Singh Dhama, Konstantinos Spiliopoulos
In this paper, we establish a Quantitative Central Limit Theorem (QCLT) for the Stochastic Gradient Descent in Continuous Time (SGDCT) algorithm, whose parameter updates are govern…
Uniform-in-time bounds for a stochastic hybrid system with fast periodic sampling and small white-noise
Shivam Singh Dhama, Konstantinos Spiliopoulos
We study the asymptotic behavior, uniform-in-time, of a non-linear dynamical system under the combined effects of fast periodic sampling with period and small white noise of si…
Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise
Shivam Dhama, Chetan D. Pahlajani
We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size , and fast periodic sampling with pe…