Related papers: Spatial risk measures and rate of spatial diversif…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
Spatial heteroskedasticity refers to stochastically changing variances and covariances in space. Such features have been observed in, for example, air pollution and vegetation data. We study how volatility modulated moving averages can…
In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…
The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent…
In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
We consider the extinction regime in the spatial stochastic logistic model in $\mathbb{R}^d$ (a.k.a. Bolker--Pacala--Dieckmann--Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space…
If an effect measure is more homogeneous than others, then its value is more likely to be stable across different subgroups or subpopulations. Therefore, it is of great importance to find a more homogeneous effect measure that allows for…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
In a spatial-temporal model, structural change and/or spatial heterogeneity can easily affect estimation of parameters. Following the spatial-temporal model in [1], we develop a nonparametric procedure for test-ing the presence of…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…