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math.PR2019★ 2 cited
On stochastic Langevin and Fokker-Planck equations: the two-dimensional case
Andrea Pascucci, Antonello Pesce
We prove existence, regularity in Hölder classes and estimates from above and below of the fundamental solution of the stochastic Langevin equation. This degenerate SPDE satisfies…
math.PR2018
The parametrix method for parabolic SPDEs
Andrea Pascucci, Antonello Pesce
We consider the Cauchy problem for a linear stochastic partial differential equation. By extending the parametrix method for PDEs whose coefficients are only measurable with respec…