3 papers
math.PR2026
Stochastic Persistence in Infinite Dimensions
Juraj Foldes, Declan Stacy
Motivated by infinite-dimensional ecological and biological models such as reaction-diffusion SPDEs and stochastic functional differential equations, we develop a general criteria…
math.PR2024
Small-time asymptotics for hypoelliptic diffusions
Juraj Földes, David P. Herzog
An inductive procedure is developed to calculate the asymptotic behavior at time zero of a diffusion with polynomial drift and degenerate, additive noise. The procedure gives rise…
math.AP2024
Probabilistic well-posedness of generalized cubic nonlinear Schrödinger equations with strong dispersion using higher order expansions
Jean-baptiste Casteras, Juraj Földes, Itamar Oliveira +1
In this paper, we study the local well-posedness of the cubic Schrödinger equation $$(i\partial_t + \mathcal{L}) u = \pm |u|^2 u \qquad \textrm{on} \quad \ I\times \mathbb{R}^d ,$…