Reflected Brownian Motion with Drift in a Wedge
Peter Lakner, Ziran Liu, Josh Reed
TL;DR
This paper analyzes reflected Brownian motion with drift in a wedge, establishing conditions for existence, uniqueness, and properties of solutions, including Markov and Feller characteristics, and explores absorption at the wedge vertex.
Contribution
It provides necessary and sufficient conditions for existence and uniqueness of solutions with drift in a wedge, and examines absorption at the vertex.
Findings
Conditions for existence and uniqueness of solutions
Solutions possess Markov and Feller properties
Probability results on absorption at the vertex
Abstract
We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provide 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Mathematical Dynamics and Fractals