Functional central limit theorem for Brownian particles in domains with Robin boundary condition
- Resource Type
- Working Paper
- Authors
- Chen, Zhen-Qing; Fan, Wai-Tong Louis
- Source
- Journal of Functional Analysis. Vol 269, No.12, 3765-3811 (2015)
- Subject
- Mathematics - Probability
Mathematical Physics
Mathematics - Analysis of PDEs
Mathematics - Functional Analysis
- Language
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 $d\geq 1$.
Comment: 33 pages