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Diffusion with Drift: The Wiener Process

In: Random Walk and Diffusion Models

Author

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  • Wolf Schwarz

    (University of Potsdam, Research Methods in Human Sciences)

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.

Suggested Citation

  • Wolf Schwarz, 2022. "Diffusion with Drift: The Wiener Process," Springer Books, in: Random Walk and Diffusion Models, chapter 0, pages 71-119, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12100-5_4
    DOI: 10.1007/978-3-031-12100-5_4
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