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arXiv · 1812.03059

Ladder Chains: A Variation of Random Walks

Chenhe Zhang·Xiang Fang
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Abstract

The authors propose a new variation of random walks called ladder chains $L(r,s,p)$. We extend concepts such as ruin probability, hitting time, transience and recurrence of random walks to ladder chain. Take $L(2,2,p)$ for instance, we find the linear difference equations that the ruin probability and the hitting time satisfy. We also prove the recurrence of a critical case $(p=\sqrt{2}-1)$. All approaches of these results can be generalized to solve similar problems for other ladder chains.

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Chenhe Zhang, Xiang Fang. 2018-12-07. Ladder Chains: A Variation of Random Walks. https://arxiv.org/abs/1812.03059

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