Diffusion with Drift: The Wiener Process

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

Chapter Chapter 4 in Random Walk and Diffusion Models, 2022, pp 71-119 from Springer

Abstract: Abstract In many applied fields, the Wiener process is the standard model of diffusive processes exhibiting a systematic drift component. In diffusion-based modeling in the behavioral and life sciences, it plays a central role, in much the same way as the normal-error general linear model with its techniques of regression, correlation, and analysis of variance plays a central role in standard applied statistics. One important reason for this prominence is that, on the one hand, the Wiener process offers sufficient structure to capture critical conceptual aspects and thus often serves as a plausible initial model. At the same time, it is still manageable enough so that tractable explicit solutions for many quantities of interest may be found. Correspondingly, for this standard model of diffusion processes, we explain in detail the techniques needed to find results (e.g., related to absorbing and reflecting barriers) relevant to many of its applications in the life sciences.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-12100-5_4

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DOI: 10.1007/978-3-031-12100-5_4

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