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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…
Local densities for a class of degenerate diffusions
Alberto Lanconelli, Stefano Pagliarani, Andrea Pascucci
We study a class of R^d-valued continuous strong Markov processes that are generated, only locally, by an ultra-parabolic operator with coefficients that are regular w.r.t. the int…
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…
Nash estimates and upper bounds for non-homogeneous Kolmogorov equations
Alberto Lanconelli, Andrea Pascucci
We prove a Gaussian upper bound for the fundamental solutions of a class of ultra-parabolic equations in divergence form. The bound is independent on the smoothness of the coeffici…