\(L^p\)-estimate for linear forward-backward stochastic differential equations (Q6113754)

This paper is concerned with coupled linear forward-backward stochastic differential equations. When the homogeneous coefficients are deterministic (the non-homogeneous coefficients can be random), the authors obtain an \(L^p\)-result \((p>2)\), including the existence and uniqueness of the \(p\)-th power integrable solution, a \(p\)-th power estimate, and a related continuous dependence property of the solution on the coefficients, for coupled linear forward-backward stochastic differential equations in the monotonicity framework over large time intervals. In order to get rid of the stubborn constraint commonly existing in the literature, i.e., the Lipschitz constant of \(\sigma\) with respect to \(z\) is very small, the authors introduce a linear transformation to overcome the difficulty on small intervals, and then ``splice'' the obtained \(L^p\)-results on many small intervals to yield the desired one on a large interval.