8 citations · 15 across the 3 of their papers we have counts for
8 papers
Deep Generative Modeling with Backward Stochastic Differential Equations
Xingcheng Xu
This paper proposes a novel deep generative model, called BSDE-Gen, which combines the flexibility of backward stochastic differential equations (BSDEs) with the power of deep neur…
General Signature Kernels
Thomas Cass, Terry Lyons, Xingcheng Xu
Suppose that and are two continuous bounded variation paths which take values in a finite-dimensional inner product space . Recent papers have introduced the truncated a…
Explicit solutions for a class of nonlinear backward stochastic differential equations and their nodal sets
Zengjing Chen, Shuhui Liu, Zhongmin Qian +1
In this paper, we investigate a class of nonlinear backward stochastic differential equations (BSDEs) arising from financial economics, and give specific information about the noda…
Optimal probabilities and controls for reflecting diffusion processes
Zhongmin Qian, Xingcheng Xu
A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting…
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'…