P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise

Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise.

Stochastic heat equation with white-noise drift

Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises

The Fokker–Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by strongly non-Gaussian noises. In particular, they yield strongly non-Gaussian anomalous diffusion which seems to be relevant in different domains of Physics....

Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

We consider the stochastic heat equation with multiplicative noise ut = 1 2 ∆u + uẆ in R+ × R , whose solution is interpreted in the mild sense. The noise Ẇ is fractional in time (with Hurst index H ≥ 1/2), and colored in space (with spatial covariance kernel f). When H > 1/2, the equation generalizes the Itô-sense equation for H = 1/2. We prove that if f is the Riesz kernel of order α, or the ...

A quasilinear stochastic partial differential equation driven by fractional white noise

We approximate the solution of a quasilinear stochastic partial differential equation driven by fractional Brownian motion BH(t); H ∈ (0, 1), which was calculated via fractional White Noise calculus, see [5].