Related papers: Survival probabilities of autoregressive processes
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…
In this paper we analyze a L\'evy process reflected at a general (possibly random) barrier. For this process we prove Central Limit Theorem for the first passage time. We also give the finite-time first passage probability asymptotics.
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and…
Let S_0=0,{S_n, n>0} be a random walk generated by a sequence of i.i.d. random variables X_1,X_2,... and let \tau^{-} be the first descending ladder epoch. Assuming that the distribution of X_1 belongs to the domain of attraction of an…
We investigate a family of multiple-stable processes that may exhibit either long-range or short-range dependence, depending on the parameters. There are two parameters for the processes, the memory parameter $\beta\in(0,1)$ and the…
We investigate the behavior of L\'{e}vy processes with convolution equivalent L\'{e}vy measures, up to the time of first passage over a high level u. Such problems arise naturally in the context of insurance risk where u is the initial…
Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in random environment and let $\left\{ S_{n},n=0,1,2,...\right\} $ be its associated random walk. It is known that if the increments of this random walk belong…
In this paper we consider two branching processes living in a joint random environment. Assuming that both processes are critical we address the following question: What is the probability that both populations survive up to a large time…
Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…
Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or…
In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival…
We consider a stochastic model for an evolving population. We show that in the presence of genotype extinctions the population dies out for a low mutation probability but may survive for a high mutation probability. This turns upside down…
For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
An extension of the RINAR(1) process for modelling discrete-time dependent counting processes is considered. The model RINAR(p) investigated here is a direct and natural extension of the real AR(p) model. Compared to classical INAR(p)…
We provide non-asymptotic bounds for first and higher order inclusion probabilities of the rejective sampling model with various size parameters. Further we derive bounds in the semi-definite ordering for matrices that collect (conditional)…