Martin boundary of a killed random walk on a half-space

Irina Ignatiouk-Robert

Martin boundary of a killed random walk on a half-space

概率论 2009-05-19 v2

作者: Irina Ignatiouk-Robert

摘要

A complete representation of the Martin boundary of killed random walks on a half-space $\Z^{d-1}\times\N^*$ is obtained. In particular, it is proved that the corresponding Martin boundary is homemorphic to the half-sphere ${\cal S}^d_+ = \{z\in\R^{d-1}\times\R_+ : |z|=1\}$ . The method is based on a combination of ratio limits theorems and large deviation techniques.

引用

@article{arxiv.math/0606439,
  title  = {Martin boundary of a killed random walk on a half-space},
  author = {Irina Ignatiouk-Robert},
  journal= {arXiv preprint arXiv:math/0606439},
  year   = {2009}
}

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