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In [4], the existence of the solution is proved for a scalar linearly growingbackward stochastic differential equation (BSDE) if the terminal value is$L\exp{\left(\mu \sqrt{2\log{(1+L)}}\,\right)}$-integrable with the positiveparameter $\mu$ being bigger than a critical value $\mu\_0$. In this note, wegive the uniqueness result for the preceding BSDE.

Uniqueness of solution to scalar BSDEs with $L\exp{\left(\mu \sqrt{2\log{(1+L)}}\,\right)}$-integrable terminal values