On Markov properties of Lévy waves in two dimensions

Robert C. Dalang and Qiang Hou

Stochastic Processes and their Applications, 1997, vol. 72, issue 2, 265-287

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 [pi]/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.

Keywords: 60G60; 60H15 (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (3)

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