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Integrability properties and limit theorems for the exit time from a cone of planar Brownian motion. (English) Zbl 1294.60103

The integrability of negative moments of the exit time of the winding process of a planar Brownian motion from a cone is established. A necessary and sufficient conditions for integrability of its positive moments is also established. Limit theorems for this exit time are proved for the shrinking/expanding cone limits, along with some generalizations. Finally, Bougerol’s identity is used in order to characterize the distribution of the exit time in terms of a certain Laplace transform.

MSC:

60J65 Brownian motion
60G51 Processes with independent increments; Lévy processes
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