2020/03/30 by Debarati Bhaumik, Marko Boon, Bhaumik, Debarati +7
Business, Management and Accounting · Earth and Planetary Sciences · Engineering · Physics and Astronomy · Social Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Marine and coastal ecosystems #NMR spectroscopy and applications #Numerical Analysis (math.NA) #Probability (math.PR) #Traffic Prediction and Management Techniques #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2003.14300
openalex publication_date 2020/03/30 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A popular method to compute first-passage probabilities in continuous-time\nMarkov chains is by numerically inverting their Laplace transforms. Past\ndecades, the scientific computing community has developed excellent numerical\nmethods for solving problems governed by partial differential equations (PDEs),\nmaking the availability of a Laplace transform not necessary here for\ncomputational purposes. In this study we demonstrate that numerical PDE problem\nsolvers are suitable for computing first passage times, and can be very\nefficient for this purpose. By doing extensive computational experiments, we\nshow that modern PDE problem solvers can outperform numerical Laplace transform\ninversion, even if a transform is available. When the Laplace transform is\nexplicit (e.g. does not require the computation of an eigensystem), numerical\ntransform inversion remains the primary method of choice.\n