Differential Equations for Probabilities and Means

Wolf Schwarz
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Wolf Schwarz: University of Potsdam, Research Methods in Human Sciences

Chapter Chapter 6 in Random Walk and Diffusion Models, 2022, pp 141-166 from Springer

Abstract: Abstract The analysis of diffusion processes with state-dependent drift or variance terms is complex and will often require recourse to numerical techniques. One reaction to this situation is to obtain information about absorption probabilities and mean first-passage times in a way that does not require the user to determine the full transition density. To this end, we describe in detail a practically important technique due to Darling and Siegert that leads to ordinary differential equations for absorption probabilities and mean first-passage times. The application of this technique is illustrated in some detail for diffusion processes involving a single or two absorbing and/or reflecting barriers.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-12100-5_6

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DOI: 10.1007/978-3-031-12100-5_6

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