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- W2972473721 abstract "In [8], the existence of the solution is proved for a scalar linearly growingbackward stochastic differential equation (BSDE) when the terminal value is$Lexp (mu sqrt{2log (1+L)} )$-integrable for a positive parameter $mu >mu _{0}$ with a critical value $mu _{0}$, and a counterexample is provided to show that the preceding integrability for $mu <mu _{0}$ is not sufficient to guarantee the existence of the solution. Afterwards, the uniqueness result (with $mu >mu _{0}$) is also given in [3] for the preceding BSDE under the uniformly Lipschitz condition of the generator. In this note, we prove that these two results still hold for the critical case: $mu =mu _{0}$." @default.
- W2972473721 created "2019-09-19" @default.
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- W2972473721 date "2019-01-01" @default.
- W2972473721 modified "2023-10-17" @default.
- W2972473721 title "Existence and uniqueness of solution to scalar BSDEs with $Lexp (mu sqrt{2log (1+L)} )$-integrable terminal values: the critical case" @default.
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- W2972473721 doi "https://doi.org/10.1214/19-ecp254" @default.
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