Stochastic wave equation with Lévy white noise

Stochastic heat equation with white-noise drift

Nonlinear stochastic equations with multiplicative Lévy noise.

The Langevin equation with a multiplicative Lévy white noise is solved. The noise amplitude and the drift coefficient have a power-law form. A validity of ordinary rules of the calculus for the Stratonovich interpretation is discussed. The solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the Stratonovich interpretation. The problem of escapin...

On Stochastic Navier-Stokes Equation Driven by Stationary White Noise

We consider an unbiased approximation of stochastic Navier-Stokes equation driven by spatial white noise. This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The nonlinear term can be characterized as the highest stochastic order approximation of the original nonlinear term u∇u. We investigate the analyti...

The Stochastic Transport Equation Driven by Lévy White Noise

In this paper we demonstrate how concepts of white noise analysis can be used to give an explicit solution to a stochastic transport equation driven by Lévy white noise.

Stochastic Euler equations of fluid dynamics with Lévy noise

In this work we prove the existence and uniqueness of pathwise solutions up to a stopping time to the stochastic Euler equations perturbed by additive and multiplicative Lévy noise in two and three dimensions. The existence of a unique maximal solution is also proved.