in this paper, we show that the conditional transform with respect to the gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. we then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

the purpose of this paper is to provide some asymptotic results for nonparametric estimator of the lorenz curve and lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. first, we show that nonparametric estimator of the lorenz curve is uniformly strongly consistent for the associated lorenz curve. also, a strong gaussian approximation for ...