[图书][B] Renewal theory for perturbed random walks and similar processes
A Iksanov - 2016 - Springer
The present book offers a detailed treatment of perturbed random walks, perpetuities, and
random processes with immigration. These objects are of major importance in modern …
random processes with immigration. These objects are of major importance in modern …
[HTML][HTML] On a skew stable Lévy process
A Iksanov, A Pilipenko - Stochastic Processes and their Applications, 2023 - Elsevier
The skew Brownian motion is a strong Markov process which behaves like a Brownian
motion until hitting zero and exhibits an asymmetry at zero. We address the following …
motion until hitting zero and exhibits an asymmetry at zero. We address the following …
On a discrete approximation of a skew stable L\'{e} vy process
C Dong, O Iksanov, A Pilipenko - arXiv preprint arXiv:2302.07298, 2023 - arxiv.org
Iksanov and Pilipenko (2023) defined a skew stable L\'{e} vy process as a scaling limit of a
sequence of perturbed at $0 $ symmetric stable L\'{e} vy processes (continuous-time …
sequence of perturbed at $0 $ symmetric stable L\'{e} vy processes (continuous-time …
Limit theorem for perturbed random walks
HL Ngo, M Peigné - arXiv preprint arXiv:1906.00440, 2019 - arxiv.org
We consider random walks perturbed at zero which behave like (possibly different) random
walks with iid increments on each half lines and restarts at $0 $ whenever they cross that …
walks with iid increments on each half lines and restarts at $0 $ whenever they cross that …
Limit behaviour of random walks on ℤm with two-sided membrane
V Bogdanskii, I Pavlyukevich… - ESAIM: Probability and …, 2022 - esaim-ps.org
We study Markov chains on ℤ m, m≥ 2, that behave like a standard symmetric random walk
outside of the hyperplane (membrane) H={0}× ℤ m− 1. The exit probabilities from the …
outside of the hyperplane (membrane) H={0}× ℤ m− 1. The exit probabilities from the …
Uniformly expanding Markov maps of the real line: exactness and infinite mixing
M Lenci - arXiv preprint arXiv:1404.2212, 2014 - arxiv.org
We give a fairly complete characterization of the exact components of a large class of
uniformly expanding Markov maps of $\mathbb {R} $. Using this result, for a class of …
uniformly expanding Markov maps of $\mathbb {R} $. Using this result, for a class of …
Demographic inference for spatially heterogeneous populations using long shared haplotypes
R Forien, H Ringbauer, G Coop - Theoretical Population Biology, 2024 - pure.mpg.de
We introduce a modified spatial Λ-Fleming–Viot process to model the ancestry of individuals
in a population occupying a continuous spatial habitat divided into two areas by a sharp …
in a population occupying a continuous spatial habitat divided into two areas by a sharp …
Functional limit theorems for the maxima of perturbed random walk and divergent perpetuities in the M 1-topology
Abstract Let (ξ 1, η 1),(ξ 2, η 2),… be a sequence of iid two-dimensional random vectors. In
the earlier article Iksanov and Pilipenko (2014) weak convergence in the J 1-topology on the …
the earlier article Iksanov and Pilipenko (2014) weak convergence in the J 1-topology on the …
Walsh's Brownian Motion and Donsker Scaling Limits of Perturbed Random Walks
I Pavlyukevich, A Pilipenko - arXiv preprint arXiv:2310.10809, 2023 - arxiv.org
In this paper, we study the Donsker scaling limit of integer-valued random walks perturbed
on a finite subset of $\mathbb Z $ called a membrane. Under very mild assumptions about …
on a finite subset of $\mathbb Z $ called a membrane. Under very mild assumptions about …
On multidimensional locally perturbed standard random walks
C Dong, A Iksanov, A Pilipenko - arXiv preprint arXiv:2312.15806, 2023 - arxiv.org
Let $ d $ be a positive integer and $ A $ a set in $\mathbb {Z}^ d $, which contains finitely
many points with integer coordinates. We consider $ X $ a standard random walk perturbed …
many points with integer coordinates. We consider $ X $ a standard random walk perturbed …