Solution
= Solution
Assume all contributing decay rates satisfy $\nu_l>0$ and the summed expression is a nonnegative density. Then
$$
\int_0^\infty p(t)\,dt=\sum_lA_l\int_0^\infty\nu_le^{-\nu_lt}\,dt=\sum_lA_l.
$$
Thus \b[$\sum_lA_l=1$ normalizes the first-passage distribution]. A zero decay rate would require separate treatment of a nonabsorbing component; eventual absorption is implicit here. Individual spectral coefficients need not all be positive, but the full density must be.