6 papers
Distribution dependent SDEs with multiplicative fractional noise
Xiliang Fan, Shao-Qin Zhang
The well-posedness is investigated for distribution dependent stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (\ff {\sq 5-1} 2,1)$…
Distribution dependent SDEs driven by fractional Brownian motions
Xiliang Fan, Xing Huang, Yongqiang Suo +1
In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H\in(1/2,1). We prove the well…
A unified approach to gradient type formulas for BSDEs and some applications
Xiliang Fan, Michael Röckner, Shao-Qin Zhang
In this paper we present a unified approach to establish gradient type formulas and Bismut type formulas for backward stochastic differential equations (BSDEs). This approach relie…
A study on the fractional Gruschin type process
Xiliang Fan, Rong Yu
In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Sin…
Moment estimates and applications for SDEs driven by fractional Brownian motion with irregular drifts
Xi-Liang Fan, Shao-Qin Zhang
In this paper, high-order moment, even exponential moment, estimates are established for the Hölder norm of solutions to stochastic differential equations driven by fractional Brow…
Density estimates for the solutions of backward stochastic differential equations driven by Gaussian processes
Xiliang Fan, Jiang-Lun Wu
The aim of this paper is twofold. Firstly, we derive upper and lower non-Gaussian bounds for the densities of the marginal laws of the solutions to backward stochastic differential…