5 papers
Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion
Eliseo Luongo, Francesco Triggiano
We study a slow-fast system of coupled two- and three-dimensional Navier-Stokes equations in which the fast component is perturbed by an additive fractional Brownian noise with Hur…
Dissipative solutions to randomly forced 3D Euler equations
Umberto Pappalettera, Francesco Triggiano
The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P…
Effective continuous equations for adaptive SGD: a stochastic analysis view
Luca Callisti, Marco Romito, Francesco Triggiano
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations fram…
Non-uniqueness of weak solutions for a logarithmically supercritical hyperdissipative Navier-Stokes system
Marco Romito, Francesco Triggiano
The existence of non-unique solutions of finite kinetic energy for the three dimensional Navier-Stokes equations is proved in the slightly supercritical hyper-dissipative setting i…
Gaussian processes based data augmentation and expected signature for time series classification
Marco Romito, Francesco Triggiano
The signature is a fundamental object that describes paths (that is, continuous functions from an interval to a Euclidean space). Likewise, the expected signature provides a statis…