<p style='text-indent:20px;'>In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in second unknown <inline-formula><tex-math id="M1">\begin{document}$ z $\end{document}</tex-math></inline-formula>. Using a linearization technique and BMO martingale theory, first apply fixed-point argument to...

A variable step size multi-block backward differentiation formula for solving stiff initial value problems of ordinary differential equations with a strategy was derived. The proposed method (VSSMBBDF) computes two approximate solution values at time per integration step. stability properties are achieved by varying the ratio in to generate more zero stable schemes. is also found be an A-Stable...

This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation cost functional LQ system is derived by technique Itô’s formula with jumps. For system, we establish equivalence between open-loop (closed-loop, resp.) solvability and existence an adapted solution to corresponding forward-backward differential...

We consider a system of semilinear partial differential equations (PDEs) with measurable coefficients and nonlinear Neumann boundary condition. then construct sequence penalized PDEs, which converges to our initial problem. Since the we may be discontinuous, use notion solution in [Formula: see text]-viscosity sense. The method is based on backward stochastic their S-tightness. This work motiva...

In this paper, we discuss a new type of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and ...