AI 中文总结
该研究针对满足分布依赖型李雅普诺夫条件的McKean-Vlasov随机微分方程，提出混合Perron-Nagumo准则证明其强解的存在性与路径wise唯一性，且给出了适用该准则但不满足经典条件的实例。
AI 中文摘要
我们建立了满足分布依赖型李雅普诺夫条件的McKean-Vlasov随机微分方程的强存在性与路径wise唯一性。在混合Perron-Nagumo条件下（该条件允许初始时刻存在不可积奇点），路径wise唯一性在满足对应李雅普诺夫估计的强解类中成立。对于存在性，我们在嵌套有界域上截断系数，构造吸收型局部弱解，通过紧性论证过渡到弱解，再应用受限Yamada-Watanabe定理得到强解。我们的存在性证明不同于经典的截断-拼接方法，本身具有研究价值。我们还提供了一个明确的例子，我们的准则适用于该例子，而该例子不满足Lipschitz、Osgood或单调性条件。
英文摘要
We establish strong existence and pathwise uniqueness for McKean-Vlasov stochastic differential equations with coefficients satisfying a distribution-dependent Lyapunov condition. Under a hybrid Perron-Nagumo condition that permits a non-integrable singularity at the initial time, pathwise uniqueness holds within the class of strong solutions satisfying the corresponding Lyapunov estimate. For existence, we truncate the coefficients on nested bounded domains, construct absorbed local weak solutions, pass to a weak solution via tightness arguments, and then apply a restricted Yamada-Watanabe theorem to obtain a strong solution. Our existence proof, different from the classical truncation-patching method, is interesting in its own right. We also provide an explicit example to which our criterion applies, while none of the Lipschitz, Osgood, or monotonicity conditions is satisfied.
Comments22 pages and 1 figure
