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Moderate deviations principle for systems of slow-fast diffusions
Matthew R. Morse, Konstantinos Spiliopoulos
In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stoch…
Stochastic Gradient Descent in Continuous Time
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…
Rare event simulation via importance sampling for linear SPDE's
Michael Salins, Konstantinos Spiliopoulos
The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial diff…
Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes
Andrew Papanicolaou, Konstantinos Spiliopoulos
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the fi…
Improving the convergence of reversible samplers
Luc Rey-Bellet, Konstantinos Spiliopoulos
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent r…
Markov processes with spatial delay: path space characterization, occupation time and properties
Michael Salins, Konstantinos Spiliopoulos
In this paper, we study one dimensional Markov processes with spatial delay. Since the seminal work of Feller, we know that virtually any one dimensional, strong, homogeneous, cont…