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Lp Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

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Abstract

In this paper, the authors establish the existence and uniqueness theorem of Lp (1 < p ≤ 2) solutions for multidimensional backward doubly stochastic differential equations (BDSDEs for short) under the p-order globally (locally) weak monotonicity conditions. Comparison theorem of Lp solutions for one-dimensional BDSDEs is also proved. These conclusions unify and generalize some known results.

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Acknowledgement

The authors would like to thank the editors and the anonymous reviewers for their insightful comments and valuable suggestions, which have helped them to improve the paper.

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China

    Dejian Tian

  2. Department of Mathematics, Hohai University, Nanjing, 210098, China

    Runyu Zhu

Authors
  1. Dejian Tian
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  2. Runyu Zhu
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Corresponding author

Correspondence to Runyu Zhu.

Additional information

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

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Tian, D., Zhu, R. Lp Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients. Chin. Ann. Math. Ser. B 42, 409–426 (2021). https://doi.org/10.1007/s11401-021-0266-5

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  • DOI: https://doi.org/10.1007/s11401-021-0266-5

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