论文标题
在具有不连续漂移系数的混合分数SDE上
On mixed fractional SDEs with discontinuous drift coefficient
论文作者
论文摘要
我们证明了溶液的存在和独特性，用于一类由标准布朗运动和分数布朗运动驱动的一类混合分数随机微分方程。此外，我们建立了具有绝对连续导数且适用于具有Lipschitz系数的混合分数随机微分方程的解决方案的函数有效的广义iTô规则，这在我们的存在和独特性方面起着关键作用。这种公式的证据是新的，依赖于在对扩散系数的轻度假设下显示法律密度的存在。
We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient.
