General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition

<p style='text-indent:20px;'>This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where generator <inline-formula> <tex-math id="M1">\begin{document}$ g $\end{document}</tex-math> </inline-formula> satisfies weak stochastic-monotonicity condition growth in state variable id="M2">\begin{document}$ y </inline-formula>, stochastic-Lipschitz id="M3">\begin{document}$ z </inline-formula>. This unifies strengthens some known works. In order to prove this result, we develop ideas techniques employed Xiao Fan [<xref ref-type="bibr" rid="b25">25</xref>] Liu et al. rid="b15">15</xref>]. particular, put forward Gronwall-type inequality Bihari-type inequality, which generalize classical ones may be useful other applications. The martingale representation theorem, Itô’s formula, BMO tool are used these two inequalities. </p>