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Random Walks in Nonhomogeneous Poisson Environment
P. 3–24.
Davydov Y., Konakov V.
In the first part of the paper we consider a "random flight" process in \(R^d\) and obtain the weak limits under different transformations of the Poissonian switching times. In the second part we construct diffusion approximations for this process and investigate their accuracy. To prove the weak convergence result we use the approach of Stroock and Varadhan (1979). We consider more general model which may be called "random walk over ellipsoids in \(R^d\)". For this model we establish the Edgeworth type expansion. The main tool in this part is the parametrix method (Konakov (2012), Konakov and Mammen (2009)).
Keywords: случайные блужданияметод параметриксаrandom walksparametrix methodrandom flightsRandom nonhomogeneous environmentDiffusion approximationслучайная неоднородная среда
Publication based on the results of:
In book
Heidelberg: Springer, 2017.
Ермолаев Е. С., Applied Network Science 2025 Vol. 10 Article 30
Recent advances in complex systems have highlighted the utility of simplicial complexes for modeling higher-order interactions, particularly in biological and physical networks. This study presents enhanced Simplex2Vec, an adaptation of the Simplex2Vec algorithm, to facilitate community detection within such structures. We compare enhanced Simplex2Vec’s efficacy against the Leiden algorithm and Spectral clustering using 7 distinct ...
Added: December 30, 2025
Skopenkov M., Ustinov A., Zaslavsky A., , in: Mathematics via Problems: Part 3: Combinatorics* 3: Combinatorics.: Providence: AMS, 2023.
Added: October 16, 2025
Заславский А. А., Skopenkov M., Ustinov A., В кн.: Элементы математики в задачах: через олимпиады и кружки—к профессии.: М.: МЦНМО, 2018.
The chapter is devoted to random walks and electrical networks. ...
Added: October 13, 2025
Баранов Д. В., Skopenkov M., Ustinov A., Математическое просвещение 2011 № 15 С. 229–230
This collection of problems is based on the project “Random walks and electric circuits” of the XXII Summer Conference of the Tournament of Cities and problem 14.12 from the problem book “Mathematical Enlightenment” (issue 14, p. 274). ...
Added: October 9, 2025
Skopenkov M., Смыкалов В., Ustinov A., Математическое просвещение 2012 № 16 С. 25–47
The article is devoted to the mathematical theory of electrical networks. ...
Added: October 9, 2025
Danilov V., Михайлова С. О., Математические заметки 2024 Т. 116 № 6 С. 881–897
В этой статье на примере случайных блужданий будет представлен метод решения параболических задач на сетке. Ввиду стохастических свойств случайных блужданий ранее полученные интерполяционные методы решения гиперболических задач (преобразование Фурье, теорема В. А. Котельникова) на сетках неприменимы. В данной статье строится формальная асимптотика фундаментального решения задачи Коши и краевых задач для параболического случайного блуждания по решетке, ...
Added: November 26, 2024
Konakov V., Menozzi S., / Series arXiv "math". 2023. No. 2312.06222.
Abstract. We prove central and local limit theorems for random walks on the Poincar´e hyperbolic space of
dimension n ě 2. To this end we use the ball model and describe the walk therein through the M¨obius addition
and multiplication. This also allows to derive a corresponding law of large numbers. ...
Added: December 12, 2023
Molchanov S., Куценко В. А., Яровая Е. Б., Успехи математических наук 2023 Т. 78 № 5(473) С. 181–182
Условия надкритичности для ветвящихся блужданий в случайной убивающей среде с единственным центром размножения. ...
Added: November 3, 2023
Konakov V., Mammen E., / Series arXiv "math". 2023. No. 2304.10673.
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 distributions approximate the stochastic performance of the algorithm. Here, we are interested in strong approximations for Robbins-Monro procedures. The main tool for ...
Added: April 24, 2023
Bitter I., Konakov V., Random Operators and Stochastic Equations 2021 Vol. 29 No. 4 P. 287–308
In this paper, we derive a stability result for L1 and L∞ perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and we do not require uniform convergence of perturbed diffusions. Instead, we require a weaker convergence condition in a special metric introduced ...
Added: November 29, 2021
Galkin S., Belmans P., Mukhopadhyay S., / Series math "arxiv.org". 2020. No. 2009.05568.
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. These graphs encode degenerations of curves to rational curves, and graph potentials encode degenerations of the moduli space of rank 2 bundles with fixed determinant. We show that the birational type of the graph potential only depends on the homotopy type of ...
Added: April 15, 2021
Боровков А. А., Cambridge University Press, 2020.
This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established ...
Added: March 30, 2021
Menozzi S., Pesce A., Zhang X., Journal of Differential Equations 2021 Vol. 272 P. 330–369
We consider non degenerate Brownian SDEs with Hölder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial Hölder continuity assumptions on the drift. Importantly, the estimates reflect the transport of ...
Added: October 31, 2020