3 papers
math.PR2026
Geometric Regime--Switching Diffusions on Stratified Riemannian Spaces with an Application to Covariance Matrices
Leonardo Marconi, Matteo Farnè, Alexander Aue
We construct geometric regime-switching diffusions, a class of Markov processes on locally compact stratified Riemannian state spaces. In contrast with classical regime-switching a…
math.DG2026
An associated bundle approach to the Bures--Wasserstein geometry of fixed rank covariance matrices
Leonardo Marconi
The Bures--Wasserstein geometry of covariance matrices provides a canonical distance on the statistical manifold of centred Gaussian measures and lies at the intersection of inform…
math.PR2024
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…