We study the statistically invariant structures of nonlinear generalized Langevin equation (GLE) with a power-law memory kernel. For broad class kernels, including those in subdiffusive regime, we construct solutions GLE using Gibbsian framework, which does not rely on existing Markovian approximations. Moreover, provide conditions decay to ensure uniqueness steady states, generalizing previous...

Fractional Langevin equation to describe anomalous diffusion. Abstract A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional ...

In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nosé-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of the conjugate momentum vector. Numerical experiments with a double well potential corroborate the as...