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

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay,…

The concept of a L\'evy subordinator is generalized to a family of non-decreasing stochastic processes, which are parameterized in terms of two Bernstein functions. Whereas the independent increments property is only maintained in the…

The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs. We show that such solutions are characterized by extremality conditions, which may…

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…

Let $(E, \| \cdot\|)$ be a Banach space such that, for some $q\geq 2$, the function $x\mapsto \|x\|^q$ is of $C^2$ class and its first and second Fr\'{e}chet derivatives are bounded by some constant multiples of $(q-1)$-th power of the norm…

The extremal t process was proposed in the literature for modeling spatial extremes within a copula framework based on the extreme value limit of elliptical t distributions (Davison, Padoan and Ribatet (2012)). A major drawback of this…

Let $\pa{X_{t}}_{t\in T}$ be a family of real-valued centered random variables indexed by a countable set $T$. In the first part of this paper, we establish exponential bounds for the deviation probabilities of the supremum $Z=\sup_{t\in…

Many practical problems involve estimating low dimensional statistical quantities with high-dimensional models and datasets. Several approaches address these estimation tasks based on the theory of influence functions, such as…

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…

We introduce a class of spatial stochastic processes in the max-domain of attraction of familiar max-stable processes. The new class is based on Cox processes and comprises models with short range dependence. We show that statistical…

The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…

This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…

Max-stable random fields provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative…

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of…

This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…

For strictly ergodic systems, we introduce the class of CF-Nil($k$) systems: systems for which the maximal measurable and maximal topological $k$-step pronilfactors coincide as measure-preserving systems. Weiss' theorem implies that such…

We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their…

In order to describe the extremal behaviour of some stochastic process $X$, approaches from univariate extreme value theory are typically generalized to the spatial domain. In particular, generalized peaks-over-threshold approaches allow…

Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity…

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…