The reliability of dynamic systems modeled by white noise excited, stochastic, ordinary di erential equations can be computed from deterministic backward Kolmogorov equations. This paper discusses and compares some numerical solution methods for boundary value problems involving backward Kolmogorov equations. The numerical examples concern single degree of freedom oscillators subjected to white...

We write explicitly the complete Lorentzian metric of a singularity-free spacetime where black hole transitions into white located in its same asymptotic region. In particular, interpolates between and horizons. The satisfies Einstein field equations up to tunneling matter giving rise is described by Oppenheimer-Snyder model, corrected with loop-quantum-cosmology techniques quantum interior geo...