arXiv
Open Access
2019
Embedding of Walsh Brownian Motion
Erhan Bayraktar
Xin Zhang
Abstrak
Let $(Z,κ)$ be a Walsh Brownian motion with spinning measure $κ$. Suppose $μ$ is a probability measure on $\mathbb{R}^n$. We characterize all the $κ$ such that $μ$ is a stopping distribution of $(Z,κ)$. If we further restrict the solution to be integrable, we show that there would be only one choice of $κ$. We also generalize Vallois' embedding, and prove that it minimizes the expectation $\mathbb{E}[Ψ(L^Z_τ)]$ among all the admissible solutions $τ$, where $Ψ$ is a strictly convex function and $(L_t^Z)_{t \geq 0}$ is the local time of the Walsh Brownian motion at the origin.
Penulis (2)
E
Erhan Bayraktar
X
Xin Zhang
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2019
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- en
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- arXiv
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- Open Access ✓