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That is, $S_n^{(2)}=S_1+S_2+ ... +S_n$, where $S_i=X_1+X_2+ ... s+X_i$. Assuming $X_1, X_2,....,X_n$ are integrable, zero-mean, i.i.d. random variables, we show that the persistence probabilities $$p_n^{(2)}:=\\PP(\\max_{1\\le i \\le n}S_i^{(2)}< 0) \\le c\\sqrt{\\frac{\\EE|S_{n+1}|}{(n+1)\\EE|X_1|}},$$ with $c \\le 6 \\sqrt{30}$ (and $c=2$ whenever $X_1$ is symmetric).  The converse inequality holds whenever the non-zero $\\min(-X_1,0)$ is bounded or when it has only finite third moment and in addition $X_1$ is squared integrable. 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