Related papers: Approximation of Excessive Backlog Probabilities o…

We study the rare event behavior of the workload process in a transitory queue, where the arrival epochs (or points) of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.)…

We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the…

In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…

We consider a one-dimensional random walk (RW) with a continuous and symmetric jump distribution, $f(\eta)$, characterized by a L\'evy index $\mu \in (0,2]$, which includes standard random walks ($\mu=2$) and L\'evy flights ($0<\mu<2$). We…

We analyze a simple random process in which a token is moved in the interval $A=\{0,...,n\$: Fix a probability distribution $\mu$ over $\{1,...,n\$. Initially, the token is placed in a random position in $A$. In round $t$, a random value…

Let $G$ be a group with a non-elementary action on a proper CAT(0) space $X$, and let $\mu$ be a measure on $G$ such that the random walk $(Z_n)_n$ generated by $\mu$ has finite second moment on $X$. Let $o$ be a basepoint in $X$, and…

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…

Given an initial (resp., terminal) probability measure $\mu$ (resp., $\nu$) on $\mathbb{R}^d$, we characterize those optimal stopping times $\tau$ that maximize or minimize the functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$,…

Consider $N$ points randomly distributed along a line segment of unitary length. A walker explores this disordered medium moving according to a partially self-avoiding deterministic walk. The walker, with memory $\mu$, leaves from the…

Let $\mathbb{\hat{E}}$ be the upper expectation of a weakly compact but non-dominated family $\mathcal{P}$ of probability measures. Assume that $Y$ is a $d$-dimensional $\mathcal{P}$-semimartingale under $\mathbb{\hat{E}}$. Given an open…

Let $\mathcal{G}(\frak{g}_1,\frak{g}_2)$ be the class of all probability distribution functions of positive random variables having the given first two moments $\frak{g}_1$ and $\frak{g}_2$. Let $G_1(x)$ and $G_2(x)$ be two probability…

We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

In this paper, we consider continuous-time quantum walks (CTQWs) on one-dimension ring lattice of N nodes in which every node is connected to its 2m nearest neighbors (m on either side). In the framework of the Bloch function ansatz, we…

In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and…

Consider a system of coalescing random walks where each individual performs random walk over a finite graph G, or (more generally) evolves according to some reversible Markov chain generator Q. Let C be the first time at which all walkers…

This paper provides the asymptotic analysis of the loss probability in the $GI/M/1/n$ queueing system as $n$ increases to infinity. The approach of this paper is alternative to that of the recent papers of Choi and Kim [2000] and Choi et al…

Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent but not necessarily identically distributed random variables. In this paper, the sufficient conditions are found under which the tail probability…

A fluid queue is a stochastic process which moves linearly with a rate that is determined by the state of a continuous-time Markov chain (CTMC). In this paper we construct an approximation to a fluid queue using a quasi birth-and-death…

For a jointly measurable probability-preserving action $\tau:\mathbb{R}^D\curvearrowright (X,\mu)$ and a tuple of polynomial maps $p_i:\mathbb{R}\to \mathbb{R}^D$, $i=1,2,...,k$, the multiple ergodic averages \[ \frac{1}{T}\int_0^T…