Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Menshikov, Mikhail V."'
Publikováno v:
Stochastic Processes and their Applications, Vol. 170 (2024), article 104260
For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return times and
Externí odkaz:
http://arxiv.org/abs/2208.12955
Publikováno v:
Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques, Vol. 59 (2023), no. 4, pp. 1813-1843
For a multidimensional driftless diffusion in an unbounded, smooth, sub-linear generalized parabolic domain, with oblique reflection from the boundary, we give natural conditions under which either explosion occurs, if the domain narrows sufficiently
Externí odkaz:
http://arxiv.org/abs/2203.00966
Publikováno v:
Annals of Applied Probability, Vol. 33 (2023), pp. 5459-5496
We study recurrence and transience for a particle that moves at constant velocity in the interior of an unbounded planar domain, with random reflections at the boundary governed by a Markov kernel producing outgoing angles from incoming angles. Our d
Externí odkaz:
http://arxiv.org/abs/2107.13976
Publikováno v:
In Stochastic Processes and their Applications April 2024 170
Publikováno v:
Latin American Journal of Probability and Mathematical Statistics, Vol. 19 (2022), pp. 493-510
We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely many cutpoints, generalizing existing results on nearest-neighbour random walks to adapted processes with bounded increments satisfyin
Externí odkaz:
http://arxiv.org/abs/2003.01684
Publikováno v:
pp 637-675, In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, Eds. M.E. Vares, R. Fern\'andez, L.R. Fontes, C.M. Newman, Progress in Probability 77, Springer, February 2021
We study a random walk (Markov chain) in an unbounded planar domain whose boundary is described by two curves of the form $x_2 = a^+ x_1^{\beta^+}$ and $x_2 = -a^- x_1^{\beta^-}$, with $x_1 \geq 0$. In the interior of the domain, the random walk has
Externí odkaz:
http://arxiv.org/abs/2001.06685
Publikováno v:
Indagationes Mathematicae, Vol. 31 (2020), no. 1, p. 117-146
Fix integers $d \geq 2$ and $k\geq d-1$. Consider a random walk $X_0, X_1, \ldots$ in $\mathbb{R}^d$ in which, given $X_0, X_1, \ldots, X_n$ ($n \geq k$), the next step $X_{n+1}$ is uniformly distributed on the unit ball centred at $X_n$, but conditi
Externí odkaz:
http://arxiv.org/abs/1902.09812
Publikováno v:
Electronic Journal of Probability, Vol. 24 (2019), article 62
We study the recurrence/transience phase transition for Markov chains on $\mathbb{R}_+$, $\mathbb{R}$, and $\mathbb{R}^2$ whose increments have heavy tails with exponent in $(1,2)$ and asymptotically zero mean. This is the infinite-variance analogue
Externí odkaz:
http://arxiv.org/abs/1806.07166
Publikováno v:
Journal of Theoretical Probability, Vol. 31 (2018), no. 3, p. 1819-1859
We study a random walk on a complex of finitely many half-lines joined at a common origin; jumps are heavy-tailed and of two types, either one-sided (towards the origin) or two-sided (symmetric). Transmission between half-lines via the origin is gove
Externí odkaz:
http://arxiv.org/abs/1610.00881
Publikováno v:
Advances in Applied Probability, Vol. 48 (2016), issue A, p. 99-118
Famously, a $d$-dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if $d \in \{1,2\}$ but transient if $d \geq 3$. Once spatial homogeneity is relaxed, this
Externí odkaz:
http://arxiv.org/abs/1506.08541