  We analyze the relaxation dynamics of Feynman-Kac path integral kernel
functions in terms of branching diffusion processes with killing. This sheds
new light on the admissible path-wise description of the relaxation to
equilibrium for conditioned Brownian motions, and diffusion processes with
absorbing boundaries, where Feynman-Kac kernels appear as the building blocks
of inferred transition probability density functions.
