Harnack inequality for stochastic heat equation driven by fractional noise with Hurst index H ?

摘要

In this short note, we establish the dimensional-free Harnack inequality for stochasticheat equation with Dirichlet boundary condition:??????? t u(t,x) = ? 2? x2 u(t,x) b(u(t,x)) ˙W H(t,x), 0 0, f (x) ∈ L2([0,1]) and WH(t,x) is the fractional noise with Hurst index H ∈(12,1) . The strong Feller property is also obtained.