Dynamical systems can often be decomposed into loosely coupled subsystems. The system of ordinary differential equations (ODEs) modelling such a problem can then be partitioned corresponding to the subsystems, and the loose couplings can be exploited by special integration methods to solve the problem using a parallel computer or just solve the problem more efficiently than by standard methods....

This paper studies the backward-forward linear-quadratic-Gaussian (LQG) games with major and minor agents (players). The state of major agent follows a linear backward stochastic differential equation (BSDE) and the states of minor agents are governed by linear forward stochastic differential equations (SDEs). The major agent is dominating as its state enters those of minor agents. On the other...

This paper is concerned with a new type of differential game problems of forward-backward stochastic systems. There are three distinguishing features: Firstly, our game systems are forward-backward doubly stochastic differential equations, which is a class of more general game systems than other forward-backward stochastic game systems without doubly stochastic terms; Secondly, forward equation...

In this paper, we study the recursive stochastic optimal control problems. The control domain does not need to be convex, and the generator of the backward stochastic differential equation can contain z. We obtain the variational equations for backward stochastic differential equations, and then obtain the maximum principle which solves completely Peng’s open problem.

The non-linear sewing lemma constructs flows of rough differential equations from a broad class approximations called almost flows. We consider that could be approximated by solutions ordinary equations, in the spirit backward error analysis. Mixing algebra and analysis, Taylor formula with remainder composition are central expansion With suitable algebraic structure on non-smooth vector fields...