A report by Professor Valentin Dmitrievich Konakov on the topic «Strong approximations for Robbins-Monroe procedures»

On September 17, 2025, the head of the International Laboratory of Stochastic Analysis and its Applications, Professor Valentin Dmitrievich Konakov, gave a report at the seminar of the Statistics group (France, Paris, CREST, Center for Research in Economics and Statistics).

Topic of the report:Strong approximations for Robbins-Monroe procedures

Abstract:The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, Gaussian limit theorems approximate the stochastic performance of the algorithm. Here, we are interested in strong approximations for Robbins-Monro procedures. The main tool for getting them are local limit theorems, that is, studying the convergence of the density of the algorithm. The analysis relies on a version of parametrix techniques for Markov chains converging to diffusions. The main difficulty that arises here is the fact that the drift is unbounded.

Presentation of the report