4 papers
Strong invariance principles for diffusions, Markov chains and their perturbations
V. Konakov, D. Kucher, E. Mammen
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts.…
Random walks on rank one symmetric spaces of noncompact type
Fedor Gnetov, Valentin Konakov
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural random walk on a symmetric space of non-compact type and rank one. This cl…
A Local Limit Theorem for Robbins-Monro Procedure
Lorick Huang, V Konakov
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 und…
Asymptotic version of the parametrix method for Markov chains converging to diffusions
I. Bitter, V. Konakov
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process…