Stochastic Ordering for Bernoulli and Normal Random Walks

Shoou-Ren Hsiau, Yi-Ching Yao

Let $(S_n^p{)}_{n\ge 0}$ be a Bernoulli random walk where each of the independent increments is either $1$ or $-1$ with probabilities $p$ and $1-p$. For $p^{\prime }$ and $p^{\prime \prime }\in [0,1]$ wit…