Related papers: Marked spatial point processes: current state and …
Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…
Multi-class event streams arise in numerous real-world applications, where uncovering structured, interpretable inter-event relationships, together with accurate prediction, remains a central challenge. Existing neural point process models…
The aim of this study is to extend the scope and applicability of the level-crossing method to discrete-time stochastic processes and generalize it to enable us to study multiple discrete-time stochastic processes. In previous versions of…
Multivariate spatial phenomena are ubiquitous, spanning domains such as climate, pandemics, air quality, and social economy. Cross-correlation between different quantities of interest at different locations is asymmetric in general. This…
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…
Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless…
An emerging area of research is the study of macroscale migration patterns as a network of nodes that represent places (e.g., countries, cities, and rural areas) and edges that encode migration ties that connect those places. In this…
We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…
We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
Marked Temporal Point Process (MTPP) has been well studied to model the event distribution in marked event streams, which can be used to predict the mark and arrival time of the next event. However, existing studies overlook that the…
We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…
Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network,…
The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used…
The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact…
We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical…
In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the…
We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice since most point pattern data consist…