Effect of a drift discontinuity on a travelling Gaussian Original Research Article

The effect of a fixed discontinuity on a travelling Gaussian density is modelled using a simple stochastic differential equation. The resulting density is represented as a one-dimensional integral of standard functions. Numerical examples are given. It is shown that the density reverts towards a Gaussian after leaving the neighbourhood of the discontinuity. The expectation and the variance of the transmitted Gaussian are estimated.