# Fractional stochastic heat equation with Hermite noise

Ciprian A. Tudor – GJM, Volume 7, Issue 2 (2022), 1-18.

We analyze the existence and several trajectorial and distributional properties of the solution to the fractional heat equation driven by a multiparameter Hermite process. We give a necessary and sufficient condition for the existence of the mild solution and we study the scaling property and the regularity of the trajectories of this solution. We also obtain a decomposition of the solution as the sum of a self-similar process with stationary increments and of another process with nice sample paths. This decomposition is used to get the limit behavior of the temporal $p$-variation of the solution. Via the $p$-variation method, we define a consistent estimator for the drift parameter of this equation.

Categories: Issue2