L^p (1 < p < 2) solutions of backward doubly stochastic differential equations with locally monotone coefficients

Abstract

The article considers the existence and uniqueness of $L^p (1<p<2)$ solutions for backward doubly stochastic differential equations (BDSDEs) under globally (locally) monotone conditions. Some useful and important prior estimates are established. By using truncation method, L^p solutions for BDSDEs under globally monotone assumptions are obtained. With the help of suitable approximation techniques, we derive the existence and uniqueness of L^p solutions for BDSDEs with locally monotone coefficients.

Keywords:

• Backward doubly stochastic differential equation
• locally monotone coefficient
• locally Lipschitz condition
• L^p solution

Acknowledgments

We thank the editor and two anonymous reviewers for very helpful comments and suggestions.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11601509).