Bull. Korean Math. Soc. 2017; 54(6): 2065-2079
Online first article July 6, 2017 Printed November 30, 2017
https://doi.org/10.4134/BKMS.b160740
Copyright © The Korean Mathematical Society.
Shengjun Fan, Huanhuan Luo
China University of Mining and Technology, China University of Mining and Technology
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
2013; 50(4): 1079-1086
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