On the convergence of a stochastic approximation procedure for estimating the quantile criterion in the case of a discontinuous distribution function

We study the almost surely convergence of a stochastic approximation procedure for the quantile criterion estimation. We take into account the case when the distribution function of the loss function has a discontinuity at a point coinciding with the quantile criterion value. We show that the procedure converges to the desired point under known standard assumptions with no additional constraints.

Presented by the member of Editorial Board: A. I. Kibzun