相关论文: Records for the moving average of a time series

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records…

Symmetric heavily tailed random walks on $Z^d, d\geq 1,$ are considered. Under appropriate regularity conditions on the tails of the jump distributions, global (i.e., uniform in $x,t, |x|+t\to\infty,$) asymptotic behavior of the transition…

In this work we consider the two-dimensional percolation model arising from the majority dynamics process at a given time $t\in\mathbb{R}_+$. We show the emergence of a sharp threshold phenomenon for the box crossing event at the critical…

We study a modified record process where the $k$'th record in a series of independent and identically distributed random variables is defined recursively through the condition $Y_k > Y_{k-1} - \delta_{k-1}$ with a deterministic sequence…

The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the…

We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…

We consider randomized dynamics over the $n$-simplex, where at each step a random set, or block, of coordinates is evenly averaged. When all blocks have size 2, this reduces to the repeated averages studied in [CDSZ22], a version of the…

We develop theory to understand an intriguing property of diffusion models for image generation that we term critical windows. Empirically, it has been observed that there are narrow time intervals in sampling during which particular…

We find that the probability distribution for the largest intervals $p(l)$ exhibits universal properties for different systems including random walk and random cutting models. In particular, $p(l)$ has an infinite set of singularities at…

It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time.…

We study the fluctuations of smooth linear statistics of Laplace eigenvalues of compact hyperbolic surfaces lying in short energy windows, when averaged over the moduli space of surfaces of a given genus. The average is taken with respect…

We consider one-dimensional discrete-time random walks (RWs) of $n$ steps, starting from $x_0=0$, with arbitrary symmetric and continuous jump distributions $f(\eta)$, including the important case of L\'evy flights. We study the statistics…

We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length $\ell$ over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and…

Universal outlier hypothesis testing refers to a hypothesis testing problem where one observes a large number of length-$n$ sequences -- the majority of which are distributed according to the typical distribution $\pi$ and a small number…

For a sequence of i.i.d. $d$-dimensional random vectors with independent continuously distributed coordinates, say that the $n$th observation in the sequence sets a record if it is not dominated in every coordinate by an earlier…

Let $\{X_n,n\ge1\}$ be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call $X_n$ a $\delta$-record if $X_n>\max\{X_1,...,X_{n-1}\}+\delta$, where $\delta$ is an integer…

A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…

We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…

We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample.

This paper investigates the asymptotic behavior of the extremes of a sequence of generalized Oppenheim random variables. Particularly, we establish conditions under which some normalized extremes of sequences arising from Oppenheim…