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Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type

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  • Sheng Jun Fan

    (China University of Mining and Technology)

Abstract

We establish a general existence and uniqueness result of $$L^1$$ L 1 solution for a multidimensional backward stochastic differential equation (BSDE for short) with generator g satisfying a one-sided Osgood condition as well as a general growth condition in y, and a Lipschitz condition together with a sublinear growth condition in z, which improves some existing results. In particular, we put forward and prove a stability theorem of the $$L^1$$ L 1 solutions for the first time. A new type of $$L^1$$ L 1 solution is also investigated. Some delicate techniques involved in the relationship between convergence in $$L^1$$ L 1 and in probability and dividing appropriately the time interval play crucial roles in our proofs.

Suggested Citation

  • Sheng Jun Fan, 2018. "Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1860-1899, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0755-3
    DOI: 10.1007/s10959-017-0755-3
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    References listed on IDEAS

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    Cited by:

    1. Kim, Kon-Gun & Kim, Mun-Chol & O, Hun, 2022. "Local existence and uniqueness of solutions to quadratic BSDEs with weak monotonicity and general growth generators," Statistics & Probability Letters, Elsevier, vol. 186(C).

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