• Corpus ID: 119155416

Representation Theorems of $\mathbb{R}$-trees and Brownian Motions Indexed by $\mathbb R$-trees

@article{Aksoy2016RepresentationTO,
  title={Representation Theorems of \$\mathbb\{R\}\$-trees and Brownian Motions Indexed by \$\mathbb R\$-trees},
  author={Asuman G{\"u}ven Aksoy and M. Alansari and Qidi Peng},
  journal={arXiv: Metric Geometry},
  year={2016}
}
We provide a new representation of an $\mathbb R$-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between the $\mathbb R$-trees with radial and river metrics, and these sets of metric rays. In stochastic analysis, these graphical representation theorems are of particular interest in identifying Brownian motions indexed by $\mathbb R$-trees. 

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