This paper established a general existence and uniqueness result of solutions for multidimensional backward stochastic differential equations (BSDEs) whose generators satisfy the weakly monotonic condition in y, which generalizes some existing results.
XU Shao-Ya
,
FAN Sheng-Jun
. A general existence and uniqueness result on multidimensional BSDEs[J]. Journal of East China Normal University(Natural Science), 2015
, 2015(1)
: 51
-60
.
DOI: 10.3969/j.issn.1000-5641.2015.01.006
PARDOUX E, PENG S. Adapted solution of a backward stochastic differential equation [J]. Systems Control Letters, 1990, 14: 55-61.
MAO X. Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients [J]. Stochastic Process and Their Applications, 1995, 58: 281-292.
PARDOUX E. BSDEs, weak convergence and homogenization of semilinear PDEs [C]. Nonlinear Analysis, Differential Equations and Control (Montreal, QC, 1998). Dordrecht: Kluwer Academic Publishers, 1999: 503-549.
BRIAND P H, DELYON B, HU Y, et al. Lp solutions of backward stochastic differential equations [J]. Stochastic Processes and Their Applications, 2003, 108: 109-129.
FAN S, JIANG L. Multidimensional BSDEs with weakly monotonic generators [J]. Acta Mathematica Sinica, English Series, 2013, 29: 1885-1906.