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Lp (p > 1) Solutions of BSDEs with Generators Satisfying Some Non-uniform Conditions in t and ω

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Abstract

This paper is devoted to the Lp (p > 1) solutions of one-dimensional backward stochastic differential equations (BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result, a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of Lp (p > 1) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.

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Authors and Affiliations

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

    Yajun Liu, Depeng Li & Shengjun Fan

Authors
  1. Yajun Liu
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  2. Depeng Li
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  3. Shengjun Fan
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Corresponding author

Correspondence to Shengjun Fan.

Additional information

This work was supported by the Fundamental Research Funds for the Central Universities (No.2017XKQY98).

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Liu, Y., Li, D. & Fan, S. Lp (p > 1) Solutions of BSDEs with Generators Satisfying Some Non-uniform Conditions in t and ω. Chin. Ann. Math. Ser. B 41, 479–494 (2020). https://doi.org/10.1007/s11401-020-0212-y

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  • DOI: https://doi.org/10.1007/s11401-020-0212-y

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