Abstract
For applications of stochastic fluid models, such as those related to wildfire spread and containment, one wants a fast method to compute time dependent probabilities. Erlangization is an approximation method that replaces various distributions at a time t by the corresponding ones at a random time with Erlang distribution having mean t. Here, we develop an efficient version of that algorithm for various first passage time distributions of a fluid flow, exploiting recent results on fluid flows, probabilistic underpinnings, and some special structures. Some connections with a familiar Laplace transform inversion algorithm due to Jagerman are also noted up front.
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Ramaswami, V., Woolford, D.G. & Stanford, D.A. The erlangization method for Markovian fluid flows. Ann Oper Res 160, 215–225 (2008). https://doi.org/10.1007/s10479-008-0309-2
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DOI: https://doi.org/10.1007/s10479-008-0309-2