Bulletin of the
Korean Mathematical Society BKMS

This paper is devoted to the minimal and maximal bounded solutions for general time interval quadratic backward stochastic differential equations with stochastic conditions. A general existence result is established by the method of convolution, the exponential transform, Girsanov's transform and a priori estimates, where the terminal time is allowed to be finite or infinite, and the generator $g$ is allowed to have a stochastic semi-linear growth and a general growth in $y$, and a quadratic growth in $z$. This improves some existing results at some extent. Some new ideas and techniques are also applied to prove it.

Keywords: backward stochastic differential equations, minimal and maximal bounded solutions, stochastic conditions, quadratic growth

MSC numbers: 60H10