6 papers
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…
Asymptotic analysis of dynamical systems driven by Poisson random measures with periodic sampling
Shivam Singh Dhama
In this article, we study the dynamics of a nonlinear system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period an…
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…
Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling
Shivam Dhama, Chetan D. Pahlajani
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency ($0 < δ\…