Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illust...Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illustrate the boundedness of solutions of a difference equation are also given.展开更多
This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator g satisfies a weak s...This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator g satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable y, and a stochastic-Lipschitz condition in the state variable z. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [25] and Liu et al. [15]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities.展开更多
基金Supported by the Program of Education Department of Sichuan Province(No.10ZA173)
文摘Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illustrate the boundedness of solutions of a difference equation are also given.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2017XKZD11)the National Natural Science Foundation of China(Grant No.12171471).
文摘This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator g satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable y, and a stochastic-Lipschitz condition in the state variable z. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [25] and Liu et al. [15]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities.
