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- M. Balázs, E. Cator, T. Seppäläinen
- 2006

We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right after its jump we prove that the variance of the last-passage time in a characteristic direction is of order t 2/3. With more general boundary conditions that… (More)

We show that, for a stationary version of Hammersley's process, with Poisson " sources " on the positive x-axis, and Poisson " sinks " on the positive y-axis, an isolated second class particle, located at the origin at time zero, moves asymptotically, with probability one, along the characteristic of a conservation equation for Hammersley's process. This… (More)

Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact… (More)

- ERIC CATOR
- 2009

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has always been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammer-sley last-passage percolation model with i.i.d. random weights, and the existence,… (More)

- E Cator, R van de Bovenkamp, P Van Mieghem
- Physical review. E, Statistical, nonlinear, and…
- 2013

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is… (More)

- Eric A. Cator, Hendrik P. Lopuhaä
- J. Multivariate Analysis
- 2010

In Cator and Lopuhaä [3] an asymptotic expansion for the MCD estimators is established in a very general framework. This expansion requires the existence and non-singularity of the derivative in a first-order Taylor expansion. In this paper, we prove the existence of this derivative for multivariate distributions that have a density and provide an explicit… (More)

Motivation. The new solvency regimes now emerging, insist that capital requirements align with the underlying (insurance) risks. This paper explains how a stochastic model built on basic assumptions is used to monitor insurance risk in order to get a clear insight in the aligned economic capital including prudence margins for loss reserves. Method. The… (More)

- Piet Van Mieghem, Eric Cator
- Physical review. E, Statistical, nonlinear, and…
- 2012

Since the Susceptible-Infected-Susceptible (SIS) epidemic threshold is not precisely defined in spite of its practical importance, the classical SIS epidemic process has been generalized to the ε-SIS model, where a node possesses a self-infection rate ε, in addition to a link infection rate β and a curing rate δ. The exact Markov equations are derived, from… (More)

- E Cator, P Van Mieghem
- Physical review. E, Statistical, nonlinear, and…
- 2013

Since mean-field approximations for susceptible-infected-susceptible (SIS) epidemics do not always predict the correct scaling of the epidemic threshold of the SIS metastable regime, we propose two novel approaches: (a) an ε-SIS generalized model and (b) a modified SIS model that prevents the epidemic from dying out (i.e., without the complicating absorbing… (More)

- E Cator, P Van Mieghem
- Physical review. E, Statistical, nonlinear, and…
- 2012

Given the adjacency matrix A of a network, we present a second-order mean-field expansion that improves on the first-order N-intertwined susceptible-infected-susceptible (SIS) epidemic model. Unexpectedly, we found that, in contrast to first-order, second-order mean-field theory is not always possible: the network size N should be large enough. Under the… (More)