A simple random walk $S_n = X_1 +\cdots +X_n$, where $P(X_i = 1) = p \not = 0.5$ and $P(X_i=-1)= q \triangleq 1-p$, admits the following probability $$P(S_n \textrm{ reaches } a \textrm{ before} -b) = \left(\frac{1-\left(\frac{q}{p}\right)^{b}}{1-\left(\frac{q}{p}\right)^{a+b}}\right),$$ for $a$ and $b$ positive integers. The expected number of steps to hit either of these boundaries is $$\frac{b}{q - p} - \left(\frac{a+b}{q-p}\right)\left(\frac{1-\left(\frac{q}{p}\right)^{b}}{1-\left(\frac{q}{p}\right)^{a+b}}\right).$$

My question is whether there are analogues to these simple expressions for positive $a$ and $b$ (not necessarily integer) when the $X_i$ are continuous i.i.d. random variables on $[-1,1]$ with a given density $f$? I'm particularly interested in a case where the $X_i$ have a finite positive mean $\mu_X > 0$.