摘要：In this paper, we consider the stochastic heat equation of the form ∂ u ∂ t = Δ α u + ∂ 2 B ∂ t ∂ x , $$\frac{\partial u}{\partial t}=\Delta_{\alpha}u+\frac{\partial ^,B}{\partial t\,\partial x}, $$ where ∂ 2 B ∂ t ∂ x $\frac{\partial^,B}{\partial t\,\partial x}$ is a fractional Brownian sheet with Hurst indices H 1 , H 2 ∈ ( 1 2 , 1 ) $H_),H_,\in(\frac),,1)$ and Δ α = − ( − Δ ) α / 2 $\Delta _{\alpha}=-(-\Delta)^{\alpha/2}$ is a fractional Laplacian operator with 1 < α ≤ 2 $1<\alpha\leq2$ . In particular, when H 2 = 1 2 $H_,=\frac),$ we show that the temporal process { u ( t , ⋅ ) , 0 ≤ t ≤ T } $\{u(t,\cdot),0\leq t\leq T\}$ admits a nontrivial p-variation with p = 2 α 2 α H 1 − 1 $p=\frac{2\alpha}{2\alpha H_)-1}$ and study its local nondeterminism and existence of the local time.
关键词：fractional Brownian sheet ; p -variation ; local nondeterminism ; local time
