Reflected Brownian motion with drift in a wedge

Peter Lakner (), Ziran Liu () and Josh Reed ()
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Peter Lakner: New York University
Ziran Liu: New York University
Josh Reed: New York University

Queueing Systems: Theory and Applications, 2023, vol. 105, issue 3, No 3, 233-270

Abstract: Abstract We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provides necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem with drift, and show that its solution possesses the Markov and Feller properties. Next, we study a version of the problem with absorption at the vertex of the wedge. In this case, we provide a condition for existence and uniqueness of a solution to the problem and some results on the probability of the vertex being reached.

Keywords: Submartingale problem; Absorbed process; RBM with drift; Markov property; Feller property; 60D99; 60J65 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09893-9

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