In this article, we propose an efficient general simulation method for diffusions that are solutions to stochastic differential equations with discontinuous coefficients and local time terms. The proposed is based on sampling from the corresponding continuous-time Markov chain approximation. contrast existing discretization schemes, approximation corresponds a spatial scheme demonstrated be par...

As an extension to the well-established stationary elliptic partial differential equation (PDE) with random continuous coefficients we study a time-dependent advection-diffusion problem, where may have spatial discontinuities. In subsurface flow model, randomness in parabolic account for insufficient measurements or uncertain material procurement, while discontinuities could represent transitio...