Embedding of Walsh Brownian motion

Erhan Bayraktar and Xin Zhang

Stochastic Processes and their Applications, 2021, vol. 134, issue C, 1-28

Abstract: Let (Z,κ) be a Walsh Brownian motion with spinning measure κ. Suppose μ is a probability measure on Rn. We first provide a necessary and sufficient condition for μ to be a stopping distribution of (Z,κ). Then if the stopped process is required to be uniformly integrable, we show that such a stopping time exists if and only if μ is balanced. Next, under the assumption of being balanced, we identify the minimal stopping times with those τ such that the stopped process Zτ is uniformly integrable. Finally, we generalize Vallois’ embedding, and prove that it minimizes the expectation E[Ψ(LτZ)] among all the admissible solutions τ, where Ψ is a strictly convex function and (LtZ)t≥0 is the local time of the Walsh Brownian motion at the origin.

Keywords: Skorokhod embedding problem; Walsh Brownian motion; Excursion theory; Vallois’ embedding (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:134:y:2021:i:c:p:1-28

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DOI: 10.1016/j.spa.2020.10.010

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