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Differential Equations for Probabilities and Means

In: Random Walk and Diffusion Models

Author

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  • Wolf Schwarz

    (University of Potsdam, Research Methods in Human Sciences)

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.

Suggested Citation

  • Wolf Schwarz, 2022. "Differential Equations for Probabilities and Means," Springer Books, in: Random Walk and Diffusion Models, chapter 0, pages 141-166, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12100-5_6
    DOI: 10.1007/978-3-031-12100-5_6
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