51 citations · 148 across the 23 of their papers we have counts for
23 papers
Optimal regularity of SPDEs with additive noise
Davar Khoshnevisan, Marta Sanz-Solé
The sample-function regularity of the random-field solution to a stochastic partial differential equation (SPDE) depends naturally on the roughness of the external noise, as well a…
A linear stochastic biharmonic heat equation: hitting probabilities
Adrián Hinojosa-Calleja, Marta Sanz-Solé
Consider the linear stochastic biharmonic heat equation on a -dimensional torus (), driven by a space-time white noise and with periodic boundary conditions: \begin{equ…
Anisotropic Gaussian random fields: Criteria for hitting probabilities and applications
Adrián Hinojosa-Calleja, Marta Sanz-Solé
We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class of gauge functions. This yields lower a…
Global solutions to stochastic wave equations with superlinear coefficients
Annie Millet, Marta Sanz-Solé
We prove existence and uniqueness of a random field solution to a stochastic wave equation in dimensions with diffusion and…
Systems of stochastic Poisson equations: hitting probabilities
Marta Sanz-Solé, Noèlia Viles
We consider a -dimensional random field that solves a system of elliptic stochastic equations on a bounded domain , with additive white…
Non elliptic SPDEs and ambit fields: existence of densities
Marta Sanz-Solé, André Süß
Relying on the method developed in [debusscheromito2014], we prove the existence of a density for two different examples of random fields indexed by $(t,x)\in(0,T]\times \Rd$. The…