Probability theory
Uniqueness of solution to scalar BSDEs with Lexpμ 0 2log(1+L)-integrable terminal values: an L 1 -solution approach
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1085-1095.

This paper deals with a class of scalar backward stochastic differential equations (BSDEs) with Lexp(μ 0 2log(1+L))-integrable terminal values for a critical parameter μ 0 >0. We show that the solution of these BSDEs is closely connected to the L 1 -solution of the BSDEs with integrable parameters. The key tool is the Girsanov theorem. This idea leads to a new approach to the uniqueness of solution and we obtain a new existence and uniqueness result under general assumptions.

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DOI: 10.5802/crmath.236
Classification: 60H10
O, Hun 1; Kim, Mun-Chol 1; Pak, Chol-Gyu 1

1 Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
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     title = {Uniqueness of solution to scalar {BSDEs} with $L\protect \qopname{}{o}{exp}\left(\mu _0\protect \sqrt{2\protect \qopname{}{o}{log}(1+L)}\right)$-integrable terminal values: an $L^1$-solution approach},
     journal = {Comptes Rendus. Math\'ematique},
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O, Hun; Kim, Mun-Chol; Pak, Chol-Gyu. Uniqueness of solution to scalar BSDEs with $L\protect \qopname{}{o}{exp}\left(\mu _0\protect \sqrt{2\protect \qopname{}{o}{log}(1+L)}\right)$-integrable terminal values: an $L^1$-solution approach. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1085-1095. doi : 10.5802/crmath.236. http://www.numdam.org/articles/10.5802/crmath.236/

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