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L1 solution to scalar BSDEs with logarithmic sub-linear growth generators ✩

Abstract : By developing the test function method and combining the localization technique, we prove existence of an L 1 solution to a one-dimensional backward stochastic differential equation (BSDE for short) with L 1 terminal condition when the generator g has a one-sided linear growth in the first unknown variable y and a logarithmic sub-linear growth in the second unknown variable z, which improves some existing results. A new idea to study existence of an adapted solution to a BSDE is given. When the generator g additionally satisfies a one-sided Osgood condition in y and a logarithmic uniform continuity condition in z, we further establish a comparison theorem for the L 1 solutions to the above BSDEs, which yields immediately the uniqueness of the solution.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03681198
Contributor : Ying Hu Connect in order to contact the contributor
Submitted on : Monday, May 30, 2022 - 10:28:59 AM
Last modification on : Wednesday, June 1, 2022 - 3:37:27 AM
Long-term archiving on: : Wednesday, August 31, 2022 - 6:17:01 PM

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  • HAL Id : hal-03681198, version 1

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Shengjun Fan, Ying Hu, Shanjian Tang. L1 solution to scalar BSDEs with logarithmic sub-linear growth generators ✩. 2022. ⟨hal-03681198⟩

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