Killed Random Processes and Heat Kernels [Erratum]

In J. Villarroel “Killed random processes and heat kernels” (Vol. 144, No. 2, August, 2005) on page 1238, the sentence before (2) should be: "We suppose that given that $\widehat B_t=x\in\mathbb{R}$ ($\widehat B_t$ took a value $x$ and hence has not yet been killed), the probability of being killed at any time $t+h>t$ is $O(h)\dots$"
On page 1239, the expression for $\zeta(t;p\mid x')$ after Eq. (6) should be:
$$ \zeta(t;p\mid x')\equiv\int f(t,x;p\mid x')\,dx=\int_0^{\infty}e^{-pz}\pi(t,z\mid x')\,dz. $$