相关论文: On a non-classical invariance principle

A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…

A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and…

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…

We set up Wigner distributions for $N$ state quantum systems following a Dirac inspired approach. In contrast to much of the work on this case, requiring a $2N\times 2N$ phase space, particularly when $N$ is even, our approach is uniformly…

The arbitrary functions principle says that the fractional part of $nX$ converges stably to an independent random variable uniformly distributed on the unit interval, as soon as the random variable $X$ possesses a density or a…

Given an equidistributed set in the whole Euclidean space, we have established in [1] that there exists a constant positive $C$ such that the observability inequality of diffusion equations holds for all $T\in]0,1[$, with an observability…

We report on a fundamental role of a non-normalized formal steady state, i.e., an infinite invariant density, in a semi-Markov process where the state is determined by the inter-event time of successive renewals. The state describes certain…

We give necessary and sufficient conditions to characterize the convergence in distribution of a sequence of arbitrary random variables to a probability distribution which is the invariant measure of a diffusion process. This class of…

We establish a sharp large deviation principle for renewal-reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle…

A strictly stationary sequence of random variables is constructed with the following properties: (i) the random variables take the values -1 and +1 with probability 1/2 each, (ii) every five of the random variables are independent, (iii)…

First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker…

In this reply, we resolve the apparent discrepancy raised in the "Comment on Inferring broken detailed balance in the absence of observable currents" [arXiv:2112.08978v1]. We stress that the non-instantaneous transition paths originate from…

In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…

We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…

Sufficiency, Conditionality and Invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to…

We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…

A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…