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Multidimensional BSDEs with weak monotonicity and general growth generators

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Abstract

This paper aims at solving a multidimensional backward stochastic differential equation (BSDE) whose generator g satisfies a weak monotonicity condition and a general growth condition in y. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonicity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition in y and the monotonicity condition with the general growth condition in y, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China

    Sheng Jun Fan

  2. College of Sciences, China University of Mining and Technology, Xuzhou, 221116, P. R. China

    Sheng Jun Fan & Long Jiang

Authors
  1. Sheng Jun Fan
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  2. Long Jiang
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Correspondence to Sheng Jun Fan.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11101422) and the Fundamental Research Funds for the Central Universities (Grant No. 2012QNA36)

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Fan, S.J., Jiang, L. Multidimensional BSDEs with weak monotonicity and general growth generators. Acta. Math. Sin.-English Ser. 29, 1885–1906 (2013). https://doi.org/10.1007/s10114-013-2128-x

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  • DOI: https://doi.org/10.1007/s10114-013-2128-x

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