Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics

In this paper we apply the method of stochastic characteristics to a Lighthill–Whitham–Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation perturbed by a standard Brownian motion and the geometric Brownian motion without drift.