English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In \cite{HuTang2018ECP}, the existence of the solution is proved for a scalarlinearly growing backward stochastic differential equation (BSDE) when theterminal value is $L\exp\left(\mu\sqrt{2\log(1+L)}\right)$-integrable for apositive parameter $\mu>\mu_0$ with a critical value $\mu_0$, and acounterexample 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\cite{BuckdahnHuTang2018ECP} for the preceding BSDE under the uniformlyLipschitz condition of the generator. In this note, we prove that these tworesults still hold for the critical case: $\mu=\mu_0$.

Existence and uniqueness of solution to scalar BSDEs with $L\exp\left(\mu\sqrt{2\log(1+L)}\right)$-integrable terminal values: the critical case