Functional central limit theorem for Brownian particles in domains with Robin boundary condition

Abstract

We rigorously derive non-equilibrium space-time fluctuation for the particle density of a system of reflected diffusions in bounded Lipschitz domains in ${\mathbb{R}}^d$. The particles are independent and are killed by a time-dependent potential which is asymptotically proportional to the boundary local time. We generalize the functional analytic framework introduced by Kotelenez [19, 20] to deal with time-dependent perturbations. Our proof relies on Dirichlet form method rather than the machineries derived from Kotelenez's sub-martingale inequality. Our result holds for any symmetric reflected diffusion, for any bounded Lipschitz domain and for any dimension $d\ge 1$.

33 pages

References in corpus (1)

• Systems of interacting diffusions with partial annihilation through membranes

Cited by in corpus (1)

• On the construction of convolution-like operators associated with multidimensional diffusion processes