accuracy of the procedure has been evaluated on the two models presented below on a batch of 1000 replications, each with $K=100.$

*Exponential case*

Let $R\sim \mathcal{E}(\lambda)$ with $\lambda=0.2$. The input parameters are $S_{\text{ini}}=5 
$ and $\delta =15\in \left[ 0.5\times \frac{1}{\lambda ^{2}},2\times \frac{1%
}{\lambda ^{2}}\right] $.

As shown in Table \[stairexp\], the relative error pertaining to the parameter $\lambda $ is roughly $25\%$, although the input parameters are somehow optimal for the method. The resulting relative error on the $10^{-3}$ quantile is $40\%.$ Indeed the parameter $\lambda $ is underestimated, which results in an overestimation of the variance $1/\lambda ^{2}$ , which induces an overestimation of the $10^{-3}$ quantile.

[|c|c|c|c|]{}\
&\
Mean & Std & Mean & Std\
-0.252 & 0.178 & 0.4064874 & 0.304\

*Gaussian case*

We now choose $R\sim \mathcal{N}(\mu,\sigma)$ with $\mu=60$ and $\sigma=10$. The value of $S_{\text{ini}}$ is set to the expectation and $\delta =7$ belongs to the interval $\left[ \frac{\sigma }{2},2\sigma \right] .$ The same procedure as above is performed and yields the results in Table \[stairgaus\].

[|c|c|c|c|c|c|]{}\
& &\
Mean & Std & Mean & Std & Mean & Std\
-0.059 & 0.034 & 1.544 & 0.903 & -1.753 & 0.983\

The expectation of $R$ 