Some properties of the solution to fractional heat equation with a fractional Brownian noise

In this paper, we consider the stochastic heat equation of the form partial derivative u/partial derivative t = Delta(alpha)u + partial derivative B-2/partial derivative t partial derivative x', where partial derivative B-2/partial derivative t partial derivative x is a fractional Brownian sheet with Hurst indices H-1, H-2 epsilon (1/2, 1) and Delta(alpha) = -(-Delta)(alpha/2) is a fractional Laplacian operator with 1 < alpha <= 2. In particular, when H-2 = 1/2 we show that the temporal process {u(t,.),0 <= t <= T} admits a nontrivial p-variation with p = 2 alpha/2 alpha H-1-1 and study its local nondeterminism and existence of the local time.