Exact temporal variations and parameter estimation for space--time fractional stochastic heat equations driven by multiplicative noise

Source abstract

We establish exact limits for the normalized temporal power variations of every fixed real order $γ\geq2$ for the mild solution to a one-dimensional space--time fractional stochastic heat equation driven by multiplicative space--time white noise. The results include the exact normalized quadratic variation and the critical power variation of order $2α/(α-β)$ as special cases. We also obtain the corresponding spatially averaged temporal variations. As applications, we construct consistent estimators for the drift parameter and for the ratio $β/α$.