Related papers: A Kernel Method for Exact Tail Asymptotics --- Ran…
Nearest neighbor random walks in the quarter plane that are absorbed when reaching the boundary are studied. The cases of positive and zero drift are considered. Absorption probabilities at a given time and at a given site are made…
This paper investigates the asymptotic behavior of Green functions associated to partially homogeneous random walks in the quadrant $Z_+^2$. There are four possible distributions for the jumps of these processes, depending on the location…
We obtain in this paper using the saddle point method the expression for the exact asymptotic for the tail of maximum of smooth (twice continuous differentiable) random field (process) distribution.
For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state $(i_0,j_0)$, we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive an exact…
We study asymptotic behavior, for large time $n$, of the transition probability of a two-dimensional random walk killed when entering into a non-empty finite subset $A$. We show that it behaves like $4 \tilde u_A(x) \tilde u_{-A}(-y) (\lg…
We study the trapping phenomenon of random walks in random environments of i.i.d. random conductances on the bonds of the grid $\mathbb{Z}^d$, the so-called random conductance model. Our main results concern the important model with…
By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.
Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been used for this task which enjoy fewer assumptions on the distributions than the…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
Let $\eta_1$, $\eta_2,\ldots$ be independent copies of a random variable $\eta$ with zero mean and finite variance which is bounded from the right, that is, $\eta\leq b$ almost surely for some $b>0$. Considering different types of the…
We study the tail asymptotics of two functionals (the maximum and the sum of the marks) of a generic cluster in two sub-models of the marked Poisson cluster process, namely the renewal Poisson cluster process and the Hawkes process. Under…
The busy period for a queue is cast as the area swept under the random walk until it first returns to zero, $B$. Encompassing non-i.i.d. increments, the large-deviations asymptotics of $B$ is addressed, under the assumption that the…
We study the distribution of the maximum $M$ of a random walk whose increments have a distribution with negative mean and belonging, for some $\gamma>0$, to a subclass of the class $\mathcal{S}_\gamma$--see, for example, Chover, Ney, and…
The semimartingale reflecting Brownian motion (SRBM) can be a heavy traffic limit for many server queueing networks. Asymptotic properties for stationary probabilities of the SRBM have attracted a lot of attention recently. However, many…
This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the `normalized' position of the walk. When the position is in the…
Prudent walks are special self-avoiding walks that never take a step towards an already occupied site, and \emph{$k$-sided prudent walks} (with $k=1,2,3,4$) are, in essence, only allowed to grow along $k$ directions. Prudent polygons are…
We consider random walks among random conductances on $\mathbb{Z}^2$ and establish precise asymptotics for the associated potential kernel and the Green's function of the walk killed upon exiting balls. The result is proven for random walks…
In the book [FIM], original methods were proposed to determine the invariant measure of random walks in the quarter plane with small jumps, the general solution being obtained via reduction to boundary value problems. Among other things, an…
We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…
Asymptotic results are derived for the number of random walks in alcoves of affine Weyl groups (which are certain regions in $n$-dimensional Euclidean space bounded by hyperplanes), thus solving problems posed by Grabiner [J. Combin. Theory…