Random Walk: Gambler's Ruin - Infinite Fortune

hbghlyj · 2023-6-3 00:58

Last edited by hbghlyj 2023-6-6 08:22Random Walk: Gambler's Ruin - Infinite Fortune
Given that one starts at $i$ dollars, how does one find the probability of getting infinitely rich/getting ruined (the complement)?

hbghlyj · 2023-6-3 01:01

我想，1减去（破产的概率）不等于（无限富有的概率）
因为很可能既不会破产也不会变得无限富有，只是在小范围内徘徊

hbghlyj · 2023-6-3 01:06

A8LectureNotes_MT22_24Sep2022.pdf page 51
$p>q$的情况有可能无限富有
Screenshot 2023-06-02 at 18-05-55 A8LectureNotes_MT22_24Sep2022.pdf.png

tommywong · 2023-6-3 06:54

佢應該係$\displaystyle P_i(x)=\sum_{n=0}^\infty \binom{2n+i}{n}x^n$嘅
寫漏嘢啫

hbghlyj · 2023-6-6 15:11

tommywong 发表于 2023-6-2 23:54
佢應該係$\displaystyle P_i(x)=\sum_{n=0}^\infty \binom{2n+i}{n}x^n$嘅
寫漏嘢啫

已修改。修改的同时把这个帖子顶了起来，而且4小时前，有人评论原回答是错的，有人发了一个新回答

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