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Running maximum of $\sum_{1\leq k\leq n} X_i$ for Cauchy random variables $X_i$
Suppose $X_i$ are $\mathrm{Cauchy}(0,~\gamma)$ IID RV's and let $S_n=X_1+\cdots+X_n$ be their sum. Does an expression exist for the CDF of the running maximum up to an index $1 \leq k \leq n$?
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