论文标题
衰减的衍生化估计值，用于非自主SDE的溶液功能
Decaying derivative estimates for functions of solutions to non-autonomous SDEs
论文作者
论文摘要
我们在跨时间的衍生物中产生统一和衰减的界限，以向后向后的kolmogorov方程与由时间依赖动力学控制的随机过程相关。在与该过程相关的过渡密度的有限时间内，这些假设对可集成性属性的假设保持，并假设在所有$ [0，\ infty）$上保持关闭或及时衰减的假设到某种静态度量。此外，我们提供了满足这样一组假设的示例。最后，通过引入辅助非自主随机过程，在McKean-Vlasov上下文中解释了结果。
We produce uniform and decaying bounds in time for derivatives of the solution to the backwards Kolmogorov equation associated to a stochastic processes governed by a time dependent dynamics. These hold under assumptions over the integrability properties in finite time of the derivatives of the transition density associated to the process, together with the assumption of remaining close over all $[0,\infty)$, or decaying in time, to some static measure. We moreover provide examples which satisfy such a set of assumptions. Finally, the results are interpreted in the McKean-Vlasov context for monotonic coefficients by introducing an auxiliary non-autonomous stochastic process.
