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Algorithms for return probabilities for stochastic fluid flows. (English) Zbl 1064.60162
Summary: 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 algorithms 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 number 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.

MSC:
60J22 Computational methods in Markov chains
60J25 Continuous-time Markov processes on general state spaces
60G17 Sample path properties
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