相关论文: An exceptional max-stable process fully parameteri…

Cohen and Kontorovich (COLT 2023) initiated the study of what we call here the Binomial Empirical Process: the maximal absolute value of a sequence of inhomogeneous normalized and centered binomials. They almost fully analyzed the case…

We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…

The distribution of block maxima of sequences of independent and identically-distributed random variables is used to model extreme values in many disciplines. The traditional extreme value (EV) theory derives a closed-form expression for…

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…

We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system…

We evaluate the dependence among the margins of a random vector with Multivariate Extreme Value distribution throughout the expected value of a range and relate this coefficient of dependence with the multivariate tail dependence. Its…

We prove a complete class theorem that characterizes \emph{all} stationary time reversible Markov processes whose finite dimensional marginal distributions (of all orders) are infinitely divisible. Aside from two degenerate cases (iid and…

Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the…

We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of…

Let $Z = (Z_t)_{t\in[0,\infty)}$ be an ergodic Markov process and, for every $n\in\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\in[0,\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of…

Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…

Max-stable processes provide natural models for the modelling of spatial extreme values observed at a set of spatial sites. Full likelihood inference for max-stable data is, however, complicated by the form of the likelihood function as it…

This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…

Extremal functions for the $n$th coefficient in the Krzy\.z conjecture are atomic singular inner functions with at most $n$ atoms. This paper gives a lower bound on the number of atoms $N$ of the form $N\geq cn$, marking progress toward…

We consider a strictly stationary sequence of random vectors whose finite-dimensional distributions are jointly regularly varying with some positive index. This class of processes includes, among others, ARMA processes with regularly…

It is well known that if a submartingale $X$ is bounded then the increasing predictable process $Y$ and the martingale $M$ from the Doob decomposition $% X=Y+M$ can be unbounded. In this paper for some classes of increasing convex functions…

Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…

Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…

We derive a necessary and sufficient condition for stochastic processes to have almost periodic finite dimensional distributions; in particular, we obtain characterizations for infinitely divisible processes to be almost periodic in terms…