Temporal variation for fractional heat equations with additive white noise

Abstract

Let u(t, x) be the solution to a stochastic heat equationwith initial condition u(0, x) ≡ 0, where B is a time-space white noise, α = -(-) α/2 is the fractional Laplacian with α ∈ (1, 2]. In this paper we study the quadratic variation of the process W α = {W α t = u(t, ·), t ≥ 0}. We construct a Banach space H of measurable functions such that the generalized quadratic covariationMoreover, we consider some related questions. MSC: 60G15; 60H05; 60H15