On Markov properties of Lévy waves in two dimensions

Markov properties of the solution to the wave equation in two spatial dimensions driven by a Lévy point process are considered. When the velocity of waves is 1, then for domains bounded by a plane, the sharp Markov property is shown to hold if and only if the angle between the plane and the time axis is at least π4. The sharp Markov property also holds for domains that are bounded polyhedra, because the boundary sigma-field is extremely large. The same is true of the germ-field of the boundary of a bounded open set, and this implies the germ-field Markov property for these sets.