Large deviations for stochastic models of two-dimensional second grade fluids driven by Lévy Noise

Weak Solutions of a Stochastic Model for Two-Dimensional Second Grade Fluids

Large Deviations for White-noise Driven, Nonlinear Stochastic Pdes in Two and Three Dimensions

We study the stochastic Allen-Cahn equation driven by a noise term with intensity √ ε and correlation length δ in two and three spatial dimensions. We study diagonal limits δ, ε→ 0 and describe fully the large deviation behaviour depending on the relationship between δ and ε. The recently developed theory of regularity structures allows to fully analyse the behaviour of solutions for vanishing ...

Stochastic nonlinear Schrödinger equations driven by a fractional noise Well posedness, large deviations and support

We consider stochastic nonlinear Schrödinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0, 1). It is also colored in space and the space correlation operator is assumed to be nuclear. We study the local well-posedness of the equation. Under adequate assumptions on the initial data, the space correlations of the noise and for some saturated ...

Strong solution for a stochastic model of two-dimensional second grade fluids : existence, uniqueness and asymptotic behaviour

We investigate a stochastic evolution equation for the motion of a second grade fluid filling a bounded domain of R. Global existence and uniqueness of strong probabilistic solution is established. In contrast to previous results on this model we show that the sequence of Galerkin approximation converges in mean square to the exact strong probabilistic solution of the problem. We also give two ...

Extending Stochastic Resonance for Neuron Models to General Lévy Noise

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Lévy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general LEvy noise models. We achieve this by showing that "large jump" discontinuities in the noise can be contr...