A. Kolesnik

activity

20132026

most citedRandom spherical hyperbolic diffusion

27 citations · 49 across the 12 of their papers we have counts for

collaborators

12 papers

math.PR2026

Exact formula for the 2-marginal second moment function of the multidimensional symmetric Markov random flight

Alexander D. Kolesnik

We consider the symmetric Markov random flight $X (t), t > 0,$ in the Euclidean space $R^{m}, m \geq 3$ , performed by a particle that moves in $R^{m}$ with constant fi…

math.PR2025

A diffusion model of surface soil pollution based on planar finite-velocity stochastic motion with random lifetime

Alexander D. Kolesnik

We present a diffusion model of surface soil pollution from a stationary source based on the symmetric stochastic motion at finite speed in the plane $R^{2}$ , also called the pl…

math.PR2025

Marginals of the planar symmetric Markov random flight on long time intervals behave like the Goldstein-Kac telegraph process

Alexander D. Kolesnik

The planar symmetric Markov random flight $X (t), t > 0,$ is represented by the stochastic motion of a particle moving with constant finite speed $c > 0$ in the Euclidean plane…

math.PR2023★ 3 cited

Series representations for the characteristic function of the multidimensional Markov random flight

Alexander D. Kolesnik

Two series representations of the characteristic function of the multidimensional symmetric Markov random flight with respect to Bessel functions and with respect to time variable,…

math.PR2019★ 17 cited

Spherically Restricted Random Hyperbolic Diffusion

Philip Broadbridge, Alexander D. Kolesnik, Nikolai Leonenko +2

This paper investigates solutions of hyperbolic diffusion equations in $R^{3}$ with random initial conditions. The solutions are given as spatial-temporal random fields. The…

stat.AP2019★ 27 cited

Random spherical hyperbolic diffusion

Phil Broadbridge, Alexander D. Kolesnik, Nikolai Leonenko +1

The paper starts by giving a motivation for this research and justifying the considered stochastic diffusion models for cosmic microwave background radiation studies. Then it deriv…

math.PR2017

Slow diffusion by Markov random flights

Alexander D. Kolesnik

We present a conception of the slow diffusion processes in the Euclidean spaces $R^{m}, m \geq 1$ , based on the theory of random flights with small constant speed that are driv…

math.PR2016★ 2 cited

Asymptotic relation for the transition density of the three-dimensional Markov random flight on small time intervals

Alexander D. Kolesnik

We consider the Markov random flight $X (t), t > 0,$ in the three-dimensional Euclidean space $R^{3}$ with constant finite speed $c > 0$ and the uniform choice of the initia…

math.PR2016

Integral equation for the transition density of the multidimensional Markov random flight

Alexander D. Kolesnik

We consider the Markov random flight $X (t)$ in the Euclidean space $R^{m}, m \geq 2,$ starting from the origin $0 \in R^{m}$ that, at Poisson-paced times, changes…

math.PR2015

Linear forms of the telegraph random processes driven by partial differential equations

Alexander D. Kolesnik

Consider $n$ independent Goldstein-Kac telegraph processes $X_{1} (t), \dots, X_{n} (t), n \geq 2, t \geq 0,$ on the real line $R$ . Each the process $X_{k} (t), k = 1, \dots, n,$ desc…

math.PR2014

The explicit probability distribution of the sum of two telegraph processes

Alexander D. Kolesnik

We consider two independent Goldstein-Kac telegraph processes $X_{1} (t)$ and $X_{2} (t)$ on the real line $R$ , both developing with finite constant speed $c > 0$ , that, at the initia…

math.PR2013

Probability Distribution Function for the Euclidean Distance Between Two Telegraph Processes

Alexander D. Kolesnik

Consider two independent Goldstein-Kac telegraph processes $X_{1} (t)$ and $X_{2} (t)$ on the real line $R$ . The processes $X_{k} (t), k = 1, 2,$ are performed by stochastic motions at…