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In this paper, we establish Girsanov's formula for $G$-Brownian motion. Peng (2007, 2008) constructed $G$-Brownian motion on the space of continuous paths under a sublinear expectation called $G$-expectation; as obtained by Denis et al.…

Probability · Mathematics 2013-02-22 Emi Osuka

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

In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous,…

Probability · Mathematics 2023-03-31 Ihsan Arharas , Siham Bouhadou , Youssef Ouknine

Using purely probabilistic methods, we prove the existence and the uniqueness of solutions fora system of coupled forward-backward stochastic differential equations (FBSDEs) with measurable, possibly discontinuous coefficients. As a…

Probability · Mathematics 2021-10-12 Kihun Nam , Yunxi Xu

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

We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…

Numerical Analysis · Mathematics 2010-06-15 David F. Anderson , Jonathan C. Mattingly

We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-R\"ockner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion.…

Probability · Mathematics 2025-07-09 Lukas Anzeletti , Khoa Lê , Chengcheng Ling

In this paper, we study forward-backward doubly stochastic differential equations driven by Brownian motions and Poisson process (FBDSDEP in short). Both the probabilistic interpretation for the solutions to a class of quasilinear…

Probability · Mathematics 2010-05-17 Qingfeng Zhu , Yufeng Shi

This article deals with the numerical resolution of backward stochastic differential equations. Firstly, we consider a rather general case where the filtration is generated by a Brownian motion and a Poisson random measure. We provide a…

Probability · Mathematics 2008-12-18 Emmanuel Gobet , Jean-Philippe Lemor

In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson point process. The…

Probability · Mathematics 2011-09-12 S. Hamadene , Y. Ouknine

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

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

This paper investigates solvability of fully coupled systems of forward-backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and…

Probability · Mathematics 2020-04-02 Peng Luo , Olivier Menoukeu-Pamen , Ludovic Tangpi

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just…

Probability · Mathematics 2017-11-23 Imen Hassairi

In this note, we extend some recent results on systems of backward stochastic differential equations (BSDEs) with quadratic growth to the case of coupled forward-backward stochastic differential equations (FBSDEs). We work in a Markovian…

Probability · Mathematics 2023-04-05 Joe Jackson

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it…

Probability · Mathematics 2022-12-09 Jun Gong , Huijie Qiao

In this paper, we study the question of existence and uniqueness of solution of neutral stochastic functional differential equations driven by G- Brownian motion (GNSFDEs in short) on Banach space driven by relaxed controls in which the…

Probability · Mathematics 2022-02-25 Nabil Elgroud , Hacene Boutabia , Amel Redjil , Omar Kebiri

We prove strong well-posedness for a class of stochastic evolution equations in Hilbert spaces H when the drift term is Holder continuous. This class includes examples of semilinear stochastic damped wave equations which describe elastic…

Probability · Mathematics 2023-06-01 Davide Addona , Federica Masiero , Enrico Priola

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…

Probability · Mathematics 2020-09-09 Yunwen Wang , Jinfeng Li

By studying parabolic equations in mixed-norm spaces, we prove the existence and uniqueness of strong solutions to stochastic differential equations driven by Brownian motion with coefficients in spaces with mixed-norm, which extends Krylov…

Analysis of PDEs · Mathematics 2020-02-21 Chengcheng Ling , Longjie Xie