Search results for "Random"
showing 10 items of 3931 documents
Extinction statistics in N random interacting species
2008
A randomly interacting N-species Lotka-Volterra system in the presence of a Gaussian multiplicative noise is analyzed. The investigation is focused on the role of this external noise into the statistical properties of the extinction times of the populations. The distributions show a Gaussian shape for each noise intensity value investigated. A monotonic behavior of the mean extinction time as a function of the noise intensity is found, while a nonmonotonic behavior of the width of the extinction time probability distribution characterizes the dynamical evolution.
$L_2$-variation of L\'{e}vy driven BSDEs with non-smooth terminal conditions
2016
We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\'{e}vy process $(X_t)_{t\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the L\'{e}vy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.
Conditional convex orders and measurable martingale couplings
2014
Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By analyzing topological properties of spaces of probability measures equipped with a Wasserstein metric and applying a measurable selection theorem, we prove a conditional version of this result for real-valued random variables conditioned on a random element taking values in a general measurable space. We also provide an analogue of the conditional martingale coupling theorem in the language of probability kernels and illustrate how this result can be appli…
Properties of the elasticity of a continuous random variable. A special look at its behavior and speed of change
2016
ABSTRACTBelzunce et al. (1995) define the elasticity for non negative random variables as the reversed proportional failure rate (RPFR). Veres-Ferrer and Pavia (2012, 2014b) interpret it in economic terms, extending its definition to variables that can also take negative values, and briefly present the role of elasticity in characterizing probability distributions. This paper highlights a set of properties demonstrated by elasticity, which shows many similar properties to the reverse hazard function. This paper pays particular attention to studying the increase/decrease and the speed of change of the elasticity function. These are important properties because of the characterizing role of e…
Elasticity as a measure for online determination of remission points in ongoing epidemics.
2020
The correct identification of change-points during ongoing outbreak investigations of infectious diseases is a matter of paramount importance in epidemiology, with major implications for the management of health care resources, public health and, as the COVID-19 pandemic has shown, social live. Onsets, peaks, and inflexion points are some of them. An onset is the moment when the epidemic starts. A "peak" indicates a moment at which the incorporated values, both before and after, are lower: a maximum. The inflexion points identify moments in which the rate of growth of the incorporation of new cases changes intensity. In this study, after interpreting the concept of elasticity of a random va…
The Psychological Science Accelerator’s COVID-19 rapid-response dataset
2023
Funder: Amazon Web Services (AWS) Imagine Grant
One-dimensional random walks with self-blocking immigration
2017
We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as $c \sqrt{t} \log t$. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.
Disorder relevance for the random walk pinning model in dimension 3
2011
We study the continuous time version of the random walk pinning model, where conditioned on a continuous time random walk Y on Z^d with jump rate \rho>0, which plays the role of disorder, the law up to time t of a second independent random walk X with jump rate 1 is Gibbs transformed with weight e^{\beta L_t(X,Y)}, where L_t(X,Y) is the collision local time between X and Y up to time t. As the inverse temperature \beta varies, the model undergoes a localization-delocalization transition at some critical \beta_c>=0. A natural question is whether or not there is disorder relevance, namely whether or not \beta_c differs from the critical point \beta_c^{ann} for the annealed model. In Birkner a…
Random walks in dynamic random environments and ancestry under local population regulation
2015
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in space-time regions where the medium is typical, we obtain a law of large numbers and an averaged central limit theorem for the walk via a regeneration construction under suitable coarse-graining. Such random walks occur naturally as spatial embeddings of ancestral lineages in spatial population models with local regulation. We verify that our assumptions hold for logistic branching random walks when the population density is sufficiently high.
Moderating effects of subgroups in linear models
1989
SUMMARY Possibilities for moderating effects of a subgrouping variable on strength or direction of an association have been much discussed by social scientists but have not been given satisfactory statistical formulations. The results concern directed measures of associations in linear models containing just three variables. Some key words: Analysis of covariance; Analysis of variance; cG-distribution; Conditional independence; Graphical chain model; Parallel regressions; Yule-Simpson paradox. 1. INTRODUCTION Linear models are commonly used as a framework to estimate and test how a continuous response variable depends on potential influencing variables. This paper is concerned with the situ…