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Stochastic averaging for a class of backward stochastic differential equations driven by both standard and fractional Brownian motions (SFrBSDEs in short), is investigated. An averaged SFrBSDEs for the original SFrBSDEs is proposed, and…

Probability · Mathematics 2021-06-04 Ibrahima Faye , Sadibou Aidara , Yaya Sagna

In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO…

Probability · Mathematics 2026-04-28 Hanwu Li , Peng Luo , Mengbo Zhu

In this paper, we study small-time asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H\in(1/2,1)$ and magnitude $\ep^H$. By building up a…

Probability · Mathematics 2022-07-05 Xiliang Fan , Ting Yu , Chenggui Yuan

In this article we investigate the controllability for neutral stochastic functional integro-differential equations with finite delay, driven by a fractional Brownian motion with Hurst parameter lesser than $1/2$ in a Hilbert space. We…

Probability · Mathematics 2018-09-26 Brahim Boufoussi , Soufiane Mouchtabih

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-posedness of this type equations, and then establish a…

Probability · Mathematics 2021-06-01 Xiliang Fan , Xing Huang , Yongqiang Suo , Chenggui Yuan

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H in (1/4; 1/2). Towards this end, we apply Doss-Sussmann representation of the solution and an…

Probability · Mathematics 2019-04-08 H. Araya , J. A. León , S. Torres

This note is devoted to show how to push forward the algebraic integration setting in order to treat differential systems driven by a noisy input with H\"older regularity greater than 1/4. After recalling how to treat the case of ordinary…

Probability · Mathematics 2009-01-15 Samy Tindel , Iván Torrecilla

This paper studies the existence and uniqueness of solution of It\^o type stochastic differential equation $dx(t)=b(t, x(t), \om)dt+\si(t,x(t), \om) d B(t)$, where $B(t)$ is a fractional Brownian motion of Hurst parameter $H>1/2$ and…

Probability · Mathematics 2016-12-20 Yaozhong Hu

We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of…

Numerical Analysis · Mathematics 2020-06-08 Yanzhao Cao , Jialin Hong , Zhihui Liu

In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator, which is of…

Probability · Mathematics 2019-09-25 Ying Hu , Xun Li , Jiaqiang Wen

We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$. Provided that the SDE has a negative top Lyapunov exponent, we show that a weak…

Probability · Mathematics 2026-03-16 Alexandra Blessing , Mazyar Ghani Varzaneh

In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…

Probability · Mathematics 2016-07-25 Johanna Garzón , Jorge A. León , Soledad Torres

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter $H>\frac 12$. Under some assumptions on the drift, we show that there is a unique solution, which has…

Probability · Mathematics 2007-11-19 Yaozhong Hu , David Nualart , Xiaoming Song

We study the discrete-time approximation for solutions of quadratic forward back- ward stochastic differential equations (FBSDEs) driven by a Brownian motion and a jump process which could be dependent. Assuming that the generator has a…

Optimization and Control · Mathematics 2012-11-28 Idris Kharroubi , Thomas Lim

For stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H>1/2$, Harnack type inequalities are established by constructing a coupling with unbounded time-dependent drift. These inequalities are applied…

Probability · Mathematics 2015-06-17 Xi-Liang Fan

In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise,…

Probability · Mathematics 2016-08-11 M. Besalú , A. Kohatsu-Higa , S. Tindel

In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale…

Computational Finance · Quantitative Finance 2009-10-13 Shige Peng , Xiaoming Xu

The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a…

Probability · Mathematics 2024-04-17 Guang Yang

In this paper, we first study one-dimensional quadratic backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs) with unbounded terminal values. With the help of a $\theta$-method of Briand and Hu [4] and…

Probability · Mathematics 2021-01-28 Ying Hu , Shanjian Tang , Falei Wang

In this paper we shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst…

Probability · Mathematics 2015-11-03 José Luís da Silva , Mohamed Erraoui , El Hassan Essaky