Searcharxiv⌕ Search

arXiv subjects

V. Konakov

Publications and source records attributed to V. Konakov.

6 recordsLinked to original sources
arXiv2026

Strong invariance principles for diffusions, Markov chains and their perturbations

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. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability of their exact pathwise coincidence on discrete time grids. Moreover, we construct such probability space that the probability of small deviation of the interpolated Markov chain from the continuous diffusion trajectory is small on the entire time interval if the perturbation is small enough.

math.PR↗
arXiv2025

Asymptotic version of the parametrix method for Markov chains converging to diffusions

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 coefficients satisfy weak regularity conditions and coincide only asymptotically. In particular, the drift coefficients considered by us can be unbounded with at most linear growth, and the estimates reflect the transfer of the terminal state by an unbounded trend through the corresponding deterministic flow. Our approach is based on the study of the uniform distance between the transition densities of a given inhomogeneous Markov chain and the limit diffusion process, and the convergence rate estimate is obtained using the classical local limit theorem and parametrix-type stability estimates.

math.PR↗
arXiv2016

The procedure of excluding of the nonlinear trend fir the models described by stochastic differential and difference equations

We consider the diffusion process and its approximation by Markov chain with nonlinear increasing trends. The usual parametrix method is not appliable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear growing trend and move to stochastic differential equation with reduced drift and diffusion coefficients. A similar procedure is considered for a Markov chain

math.PR↗
arXiv2015

Weak Error for Continuous Time Markov Chains Related to Fractional in Time P(I)DEs

We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential Equations (P(I)DEs). Namely, we consider equations involving a time fractional derivative of Caputo type and a spatial operator corresponding to the generator of a non degenerate Brownian or stable driven Stochastic Differential Equation (SDE).

math.PR↗
arXiv2014

Local limit theorems for Markov chains with trend component of linear growth

We consider a sequence of Markov chains weakly convergent to a diffusion. We suppose that a drift term contains a linearly increasing component. The usual parametrix method fails because of this unbounded drift term. We show how to modify the parametrix method to obtain local limit theorems for this case.

math.PR↗