Related papers: Fat-Tailed Distributions and Levy Processes
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
In this paper we characterise the propensity of big capital investments to systematically deliver poor outcomes as "fragility," a notion suggested by Nassim Taleb. A thing or system that is easily harmed by randomness is fragile. We argue…
We consider stochastic growth models to represent population subject to catastrophes. We analyze the subject from different set ups considering or not spatial restrictions, whether dispersion is a good strategy to increase the population…
The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect…
Recent advances in time series, where deterministic and stochastic modelings as well as the storage and analysis of big data are useless, permit a new approach to short-term traffic flow forecasting and to its reliability, i.e., to the…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
Biological systems perform an astonishing array of dynamical processes -- including development and repair, regulation, behavior and motor control, sensing and signaling, and adaptation, among others. Powered by the transduction of stored…
In nearly all concepts invoked or proposed to change or shield gravity it is intuitively assumed that manipulation of gravity automatically leads to a breakthrough for propulsion. In this study it is shown, that even if gravity could be…
Analysis of demographic catastrophes shows that, with the exception of perhaps only two critical events, they were too weak to influence the growth of human population. These results reinforce the conclusion that the concept of the Epoch of…
Based on realistic estimates of geophysical conditions it is demonstrated that by practical means; (1) the intensity of a hurricane can be diminished before making landfall; (2) and other circumstances, a potential hurricane might be…
Recently, different dispersion strategies in population models subject to geometric catastrophes have been considered as strategies to improve the chance of po\-pu\-lation's survival. Such dispersion strategies have been contrasted with the…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
This paper addresses the challenges of giving a causal interpretation to vector autoregressions (VARs). I show that under independence assumptions VARs can identify average treatment effects, average causal responses, or a mix of the two,…
Every driver knows that severe weather conditions cause traffic congestions. In many cases there is no direct reason for the congestion, and people tend to attribute it to the slow driving mode. Our computational study shows that the slow…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Applying a modification of Extreme value Theory (thanks to a dual distribution technique by the authors on data over the past 2,500 years, we show that pandemics are extremely fat-tailed in terms of fatalities, with a marked potentially…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…