We study a symmetric diffusion X on ℝd in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched local central limit theorem for X, under some moment conditions on the environment; the key tool is a local parabolic Harnack inequality obtained with Moser iteration technique.
- Diffusions in random environment
- Harnack inequality
- Local central limit theorem
- Moser iteration