Related papers: Records for Some Stationary Dependent Sequences
We consider multivariate copula-based stationary time-series under Gaussian subordination. Observed time series are subordinated to long-range dependent Gaussian processes and characterized by arbitrary marginal copula distributions. First…
Let $X_1,~X_2,\cdots$ be a sequence of i.i.d random variables which are supposed to be observed in sequence. The $n$th value in the sequence is a $k-record~value$ if exactly $k$ of the first $n$ values (including $X_n$) are at least as…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…
We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise.…
Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…
Let $(X_{n,t})_{t=1}^{\infty}$ be a stationary absolutely regular sequence of real random variables with the distribution dependent on the number~$n$. The paper presents sufficient conditions for the asymptotic normality (for $n\to\infty$…
We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $X_{k:n}$ of a random sample of size $n$ from a continuous distribution $F$. For central and intermediate cases,…
In this paper, we study the asymptotic relation between the maximum of acontinuous order statistics process formed by stationary Gaussian processesand the maximum of this process sampled at discrete time points. It is shown that, these two…
It is shown that statistics of records for time series generated by random walks are independent of the details of the jump distribution, as long as the latter is continuous and symmetric. In N steps, the mean of the record distribution…
We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
We study the statistics of the number of records $R_n$ for a symmetric, $n$-step, discrete jump process on a $1D$ lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability…
We consider a bivariate process $X_t=(X^1_t,X^2_t)$, which is observed on a finite time interval $[0,T]$ at discrete times $0,\Delta_n,2\Delta_n,....$ Assuming that its two components $X^1$ and $X^2$ have jumps on $[0,T]$, we derive tests…
We investigate records in a growing sequence of identical and independently distributed random variables. The record equals the largest value in the sequence, and our focus is on the increment, defined as the difference between two…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
This paper concerns the instantaneous frequency (IF) of continuous-time, zero-mean, complex-valued, proper, mean-square differentiable nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for…
We study exit times from a set for a family of multivariate autoregressive processes with normally distributed noise. By using the large deviation principle, and other methods, we show that the asymptotic behavior of the exit time depends…