Regular Diffusion and Stochastic Differential Equation with Generalized Drift

Wenjie Sun ()
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Wenjie Sun: Tongji University

Journal of Theoretical Probability, 2025, vol. 38, issue 2, 1-30

Abstract: Abstract In this paper, we shall discuss some relations between the one-dimensional regular diffusion and stochastic differential equation with generalized drift. We give a necessary and sufficient condition for a regular diffusion to satisfy a stochastic differential equation with measure-valued drift. We also give a sufficient condition for a regular diffusion to satisfy a stochastic differential equation with distributional drift. Several examples are presented.

Keywords: Regular diffusion; Dirichlet form; Stochastic differential equation; Measure-valued drift; Distributional drift; 60H10; 60J46; 60J60 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01413-0

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