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<p>In this article, we discuss a class of doubly perturbed distribution dependent stochastic differential equations (SDEs). We give some sufficient conditions to ensure the existence and uniqueness of solutions to the considered equations under some weak conditions, where a convex combination of the Nagumo and Osgood conditions is taken into consideration. Meanwhile, our results extend the classical hypothesis ∣<i>α</i>∣ + ∣<i>β</i>∣ &lt; 1 on the perturbed intensity <i>α</i> and <i>β</i> to the generalized case. And then, we study the stability properties in regard to the initial value and coefficients.</p>

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Doubly Perturbed Distribution Dependent Stochastic Differential Equation

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Zhi Li,
  • Ping He,
  • Liping Xu,
  • Litan Yan

摘要

In this article, we discuss a class of doubly perturbed distribution dependent stochastic differential equations (SDEs). We give some sufficient conditions to ensure the existence and uniqueness of solutions to the considered equations under some weak conditions, where a convex combination of the Nagumo and Osgood conditions is taken into consideration. Meanwhile, our results extend the classical hypothesis ∣α∣ + ∣β∣ < 1 on the perturbed intensity α and β to the generalized case. And then, we study the stability properties in regard to the initial value and coefficients.