DONSKER-TYPE THEOREM FOR BSDES

By P. Briand, Bernard Delyon, J. Mémin. 2001

120 citations recorded by the source corpus.

This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Our approach is based upon the notion of ``convergence of filtrations'' and covers the case of a $(y,z)$-dependent generator.

Subfields: Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/f01030229a885798e2d281cfbb994714530000cd

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Citations in the corpus

Discrete time approximation of decoupled Forward-Backward SDE with jumps (2008, methodology): “Observe that, in opposition to algorithms based on the approximation of the Brownian motion by discrete processes taking a finite number of possible values (see [1], [ 8 ], [9], [10]”
Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations (2004, methodology): “Discrete-time scheme based on the approximation of the Brownian motion by some discrete process have been considered in [10], [12], [ 8 ], [1] and [22].”
A numerical scheme for BSDEs (2004, methodology): “Recently, Briand– Delyon–Mémin [5] and Ma–Protter–San Martin–Torres [14] proposed some numerical methods for BSDEs with path-dependent terminal values.”
A regression-based Monte Carlo method to solve backward stochastic differential equations (2005, methodology): “We should also mention the works by Ma, Protter, San Martin and Soledad [21] and Briand, Delyon and Mémin [7], where the Brownian motion is replaced by a scaled random walk.”
On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights (2010, background): “The focus of this paper is on obtaining approximations for the process Y .”
Error estimates of the $\theta$-scheme for backward stochastic differentialequations (2009, methodology): “Weak convergence of these numerical solutions for BSDEs was obtained in [4, 17].”
Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations (2006, methodology): “Compared to random walk approximations (Briand et al. 2001; Ma et al. 2002), we establish a rate of convergence.”
On the robustness of backward stochastic differential equations (2002, background): “Under the assumptions, the sequence (Mn; Nn) satis@es the uniform tightness (UT) condition; cf Proposition 1:5 (b) of M, emin and S lomi, nski (1991) (for an English reference, see Section 7 of Kurtz and Protter, 1996).”
Malliavin calculus for backward stochastic differential equations and application to numerical solutions (2011, result): “We should also mention the works by Briand, Delyon and Mémin [5] and Ma et al.”