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Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem
Justin Sirignano, Konstantinos Spiliopoulos
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in…
Large deviations and averaging for systems of slow--fast stochastic reaction--diffusion equations
Wenqing Hu, Michael Salins, Konstantinos Spiliopoulos
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow comp…
Discrete-Time Statistical Inference for Multiscale Diffusions
Siragan Gailus, Konstantinos Spiliopoulos
We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We const…
Importance sampling for metastable and multiscale dynamical systems
Konstantinos Spiliopoulos
In this article, we address the issues that come up in the design of importance sampling schemes for rare events associated to stochastic dynamical systems. We focus on the issue o…