4 papers · 1 filter
Lévy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory
Zhongmin Qian, Xingcheng Xu
This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem,…
Rough Path Renormalization from Stratonovich to Itô for Fractional Brownian Motion
Zhongmin Qian, Xingcheng Xu
This paper develops an Itô-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters \( H \in (\frac{1}{3}, \frac{1}{2}] \), using the Lyons…
Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker-Planck Equations
Zhongmin Qian, Panpan Ren, Feng-Yu Wang
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficient…
Mean field equations arising from random vortex dynamics
Jiawei Li, Zhongmin Qian
We consider Mckean-Vlasov type stochastic differential equations with multiplicative noise arising from the random vortex method. Such an equation can be viewed as the mean-field l…