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<p>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. </p>

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Regular Diffusion and Stochastic Differential Equation with Generalized Drift

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Wenjie Sun

摘要

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.