Fractional stochastic heat equation with Hermite noise

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

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• janvier 12, 2023
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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.

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Received: May 18, 2021
Accepted: September 26, 2021
Revised: October 16, 2021
Published online: December 30, 2022

Authors:

Ciprian A. Tudor
Laboratoire Paul Painlevé,
Université de Lille,
F-59655 Villeneuve d'Ascq, France.

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