论文标题
完全亚临界体制中的分数SDE的解决方案理论
Solution theory of fractional SDEs in complete subcritical regimes
论文作者
论文摘要
我们考虑由分数布朗运动驱动的随机微分方程（SDE），其漂移系数允许在缩放意义上任意接近临界性。我们开发了一种全面的解决方案理论，其中包括强大的存在，逐路的唯一性，差异性的解决方案流，malliavin的可分差性和$ρ$ - 射出性。结果，我们还可以处理McKean-Vlasov，运输和连续性方程。
We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that includes strong existence, path-by-path uniqueness, existence of a solution flow of diffeomorphisms, Malliavin differentiability and $ρ$-irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations.
