On Markov properties of Lévy waves in two dimensions

Abstract

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 π 4 . 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.