6 papers
The Tricomi equation in the hyperbolic half plane under additive space-time Gaussian White Noise perturbation
Enrico Bernardi, Alberto Lanconelli
We study the Cauchy problem for the Tricomi equation perturbed by space-time Gaussian White Noise. To prove existence and uniqueness of the solution, we employ a Fourier transform…
Regularization by noise for Gevrey well-posedeness of a weakly hyperbolic operator
Enrico Bernardi, Alberto Lanconelli
We present an example of a linear partial differential equation whose Cauchy problem becomes well-posed when perturbed by noise. Specifically, we make clear how a suitable multipli…
A note on Tricomi-type partial differential equations with white noise initial condition
Enrico Bernardi, Alberto Lanconelli
We study a class of Tricomi-type partial differential equations previously investigated in [28]. Firstly, we generalize the representation formula for the solution obtained there b…
On some stochastic hyperbolic equations with symplectic characteristics
Enrico Bernardi, Leonardo Marconi
We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extend…
Non trivial optimal sampling rate for estimating a Lipschitz-continuous function in presence of mean-reverting Ornstein-Uhlenbeck noise
Enrico Bernardi, Alberto Lanconelli, Christopher S. A. Lauria +1
We examine a mean-reverting Ornstein-Uhlenbeck process that perturbs an unknown Lipschitz-continuous drift and aim to estimate the drift's value at a predetermined time horizon by…
A Novel Theoretical Framework for Exponential Smoothing
Enrico Bernardi, Alberto Lanconelli, Christopher S. A. Lauria
Simple Exponential Smoothing is a classical technique used for smoothing time series data by assigning exponentially decreasing weights to past observations through a recursive equ…