Markovian Quadratic BSDEs with an Unbounded Sub-quadratic Growth

This paper is devoted to the solvability of Markovian quadratic backward s-tochastic differential equations (BSDEs for short) with bounded terminal conditions. The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z. The existence and uniqueness results are given to these BSDEs. As an application, an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.