Systems Driven by Colored Poisson Noise: Unified Colored Noise Approximation

In this paper, unified colored noise approximation is extended to treat the systems driven by Poisson colored noise χ = ν(χ) + gε_cp(t). We arrive the evolution equation of the probability distribution pi(x, r) and the stationary probability distribution pt (χ, Υ). These equations are valid only if γ(χ,Υ) ≡ γ^-1/21 - ΥG(χ)/g(χ)] (G(χ) ≡ v'(χ)g(χ) - v(g)g'(χ)) is large enough (positive) and t >> Υ/γ(χ, Υ), but Υ is not restricted. As an application, we derive the nonlinear relaxation time (NLRT) for the processes driven by Poisson colored noise and evduate the NLRT for the approximative Ginzburg-Landon model under small Υ.