Algorithms for return probabilities for stochastic fluid flows

Abstract

We consider several known algorithms and introduce some new algorithms that can be used to calculate the probability of return to the initial level in the Markov stochastic fluid flow model. We give the physical interpretations of these algorithim within the fluid flow environment. The rates of convergence are explained in terms of the physical properties of the fluid flow processes. We compare these algorithms with respect to the numbers of iterations required and their complexity. The performance of the algorithms depends on the nature of the process considered in the analysis. We illustrate this with examples and give appropriate recommendations.