Related papers: Statistical Distributions of Earthquake Numbers: C…
Declustering aims to divide earthquake catalogs into independent events (mainshocks), and dependent (clustered) events, and is an integral component of many seismicity studies, including seismic hazard assessment. We assess the effect of…
The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
Based on recent results in extreme value theory, we use a new technique for the statistical estimation of distribution tails. Specifically, we use the Gnedenko-Pickands-Balkema-de Haan theorem, which gives a natural limit law for…
Spatiotemporal clustering of earthquake events is a generally-established fact, and is important for designing models and assessment techniques in seismicity. Here, we investigate how this behavior can manifest in the statistical…
We study earthquake interval time statistics, paying special attention to inter-occurrence times in the two-dimensional (2D) stick-slip (block-slider) model. Inter-occurrence times are the time interval between successive earthquakes on all…
The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the Dirichlet Process, is increasingly being used for probabilistic modelling in discrete areas such as language technology, bioinformatics, and image analysis. There is…
This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on the model already presented by Bruss (1984 a), refined and…
To accurately quantify landslide hazard in a region of Turkey, we develop new marked point process models within a Bayesian hierarchical framework for the joint prediction of landslide counts and sizes. To accommodate for the dominant role…
In recent years, considerable attention has been paid to research and development methods able to assess the seismic energy propagation on the territory. The seismic energy propagation is strongly related to the complexity of the source and…
Motivated by its potential application to earthquake statistics, we study the exactly self-similar branching process introduced recently by Vere-Jones, which extends the ETAS class of conditional branching point-processes of triggered…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
We consider stochastic growth models to represent population dynamics subject to geometric catastrophes. We analyze different dispersion schemes after catastrophes, to study how these schemes impact the population viability and comparing…
We provide a general model for Brownian motions on metric graphs with interactions. In a general setting, for (sticky) Brownian propagations on edges, our model provides a characterization of lifetimes and holding times on vertices in terms…
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
Catastrophes of all kinds can be roughly defined as short duration-large amplitude events following and followed by long periods of "ripening". Major earthquakes surely belong to the class of 'catastrophic' events. Because of the space-time…
The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle…
Based on the geodynamics, an earthquake does not take place until the momentum-energy excess a faulting threshold value of rock due to the movement of the fluid layer under the rock layer and the transport and accumulation of the momentum.…
Earthquake occurrence is notoriously difficult to predict. While some aspects of their spatiotemporal statistics can be relatively well captured by point-process models, very little is known regarding the magnitude of future events, and it…