More General Diffusion Processes

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

Chapter Chapter 5 in Random Walk and Diffusion Models, 2022, pp 121-140 from Springer

Abstract: Abstract A central characteristic of the Wiener process is that its drift and variance are independent of the state (position) that the process currently occupies. In some contexts, these assumptions can be too restrictive, and then more flexible models incorporating possibly state-dependent drift or variance terms are more suitable. We describe the conceptual extensions needed to this end and present formal techniques to deal with this more general situation, such as Siegert’s equation for first-passage times. These techniques are then illustrated by various examples, such as the Ornstein–Uhlenbeck and the Fisher–Wright processes.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-12100-5_5

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DOI: 10.1007/978-3-031-12100-5_5

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