Bismut公式用于具有奇异相互作用的DDSDEs的内导数

Bismut公式与Dirichlet半群的梯度估计及其在奇异 Killed DDSDEs 中的应用

Bismut Formula and Gradient Estimates for Dirichlet Semigroups with Application to Singular Killed DDSDEs

本文通过建立Dirichlet半群在规则域上的局部Bismut公式，推导出具有奇异漂移的 Killed SDEs 的梯度估计，并应用该结果界定了Killed DDSDEs 解的总变差距离。

分布依赖型随机微分方程的外导数公式

Extrinsic Derivative Formula for Distribution Dependent SDEs

该研究建立了分布依赖型随机微分方程外导数的Bismut型公式，并通过非退化、退化两类分布依赖随机微分方程例证了主要结果。

Strong and weak convergence for averaging principle of DDSDE with singular drift

In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized $L^p$ spaces. Using Zvonkin's transformation and estimates for solutions to Kolmogorov equations, we prove that the solutions of the original system strongly and weakly converge to the solution of the averaged system as the time scale $\eps$ goes to zero. Moreover, we obtain rates of the strong and weak convergence that depend on $p$ respectively.

Bismut Formula for Intrinsic/Lions Derivatives of Distribution Dependent SDEs with Singular Coefficients

By using distribution dependent Zvonkin's transforms and Malliavin calculus, the Bismut type formula is derived for the intrinisc/Lions derivatives of distribution dependent SDEs with singular drifts, which generalizes the corresponding results derived for classical SDEs and regular distribution dependent SDEs.

Sensitivity Analysis with respect to a Stock Price Model with Rough Volatility via a Bismut-Elworthy-Li Formula for Singular SDEs

In this paper, we show the existence of unique Malliavin differentiable solutions to SDE`s driven by a fractional Brownian motion with Hurst parameter H<1/2 and singular, unbounded drift vector fields, for which we also prove a stability result. Further, using the latter results, we propose a stock price model with rough and correlated volatility, which also allows for capturing regime switching effects. Finally, we also derive a Bismut-Elworthy-Li formula with respect to our stock price model for certain classes of vector fields.

所有变量均具有奇异性的 McKean-Vlasov 随机微分方程的 Log-Harnack 不等式与 Bismut 公式

Log-Harnack Inequality and Bismut Formula for McKean-Vlasov SDEs with Singularities in all Variables

本文在漂移项于时间-空间可积且分布连续性弱于 Dini 的条件下，为所有变量均具有奇异性的 McKean-Vlasov 随机微分方程建立了 log-Harnack 不等式和 Bismut 公式，显著推广了现有结果。