world:random-walk
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world:random-walk [2020/04/22 18:40] rdouc [Other method] |
world:random-walk [2023/04/18 14:58] (current) rdouc [Statement] |
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| <WRAP center round box 80%> | <WRAP center round box 80%> | ||
| - | Let $(U_i)$ be iid Rademacher random variables, i.e. $U_i=1$ or $-1$ with probability $1/2$ and set $S_i=\sum_{j=1}^iU_j$ the associated partial sum. Define $\Delta=\inf\set{t>0}{S_t=0}$. Show that $S_n$ returns to 0 with probability one. What is the law of $\Delta$? | + | Let $(U_i)$ be iid Rademacher random variables, i.e. $U_i=1$ or $-1$ with probability $1/2$ and set $S_i=\sum_{j=1}^iU_j$ the associated partial sum. Define $\Delta=\inf\set{t>0}{S_t=0}$. Show that $S_n$ returns to $0$ with probability one. What is the law of $\Delta$? |
| </WRAP> | </WRAP> | ||
world/random-walk.1587573630.txt.gz · Last modified: 2022/03/16 01:37 (external edit) · Currently locked by: 114.119.142.125
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