The Stochastic Heat Equation Driven by a Gaussian Noise: Germ Markov Property

Let u = {u(t, x); t ∈ [0, T ], x ∈ R} be the process solution of the stochastic heat equation ut = ∆u+ Ḟ , u(0, ·) = 0 driven by a Gaussian noise Ḟ , which is white in time and has spatial covariance induced by the kernel f . In this paper we prove that the process u is locally germ Markov, if f is the Bessel kernel of order α = 2k, k ∈ N+, or f is the Riesz kernel of order α = 4k, k ∈ N+.