#### Filter Results:

- Full text PDF available (27)

#### Publication Year

2004

2017

- This year (2)
- Last 5 years (15)
- Last 10 years (24)

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- 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)

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)

- 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)

- 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)

- 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)

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