相关论文: A necessary and sufficient condition for convergen…

We show that the percentile-percentile (P-P) process constructed from an independent and identically distributed sample of pairs converges in distribution in $L^1[0,1]$ if and only if the associated P-P curve is absolutely continuous. When…

For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…

We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.

We show that a necessary and sufficient condition for the sum of iid random vectors to converge (under appropriate shifting and scaling) to a multivariate Gaussian distribution is that the truncated second moment matrix is slowly varying at…

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…

Consider a class of probability distributions which is dense in the space of all probability distributions on $\mathbb{R}^{d}$ with respect to weak convergence, for every $d\in\mathbb{N}$. Then, we construct various explicit classes of…

Our goal is to find a necessary and sufficient condition on the consensus over a random network, generated by i.i.d. stochastic matrices. We show that the consensus problem in three different convergence modes (almost surely, in…

We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…

For a uniform process $\{ X_t: t\in E\}$ (by which $X_t $ is uniformly distributed on $(0,1)$ for $t\in E$) and a function $w(x)>0$ on $(0,1)$, we give a sufficient condition for the weak convergence of the empirical process based on $\{…

A continuous-time particle system on the real line satisfying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We…

The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of, nonreversible stationary distributions. In the case of an…

A necessary and sufficient condition for a L\'evy process $X$ to stay positive, in probability, near 0, which arises in studies of Chung-type laws for $X$ near 0, is given in terms of the characteristics of $X$.

When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample, since we do not have a sample from the target. These and other considerations motivate the…

We study the rate of convergence of the Mallows distance between the empirical distribution of a sample and the underlying population. The surprising feature of our results is that the convergence rate is slower in the discrete case than in…

The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a…

We consider the problem of the convergence of the so-called Le Page series in the Skohorod space $\bbD^d=\bbD([0,1],\bbR^d)$ and provide a simple criterion based on the moments of the increments of the random process involved in the series.…

Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first…

An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…

In this paper the sufficient conditions for convergence in Skorokhod space $D[0,1]$ of sequence of random processes with random time substitution are obtained.

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…