Estimating population size from multiple recapture experiments

AbstractThe size of a closed population is to be estimated using data from a multiple recapture study in either continuous or discrete time. Here the use of maximum likelihood raises computational problems. However, a family of martingale estimating functions related to the score function is shown to produce convenient simple estimators with good asymptotic efficiency relative to the maximum likelihood estimator

The Multidimensional Study of Viral Campaigns as Branching Processes

Viral campaigns on the Internet may follow variety of models, depending on the content, incentives, personal attitudes of sender and recipient to the content and other factors. Due to the fact that the knowledge of the campaign specifics is essential for the campaign managers, researchers are constantly evaluating models and real-world data. The goal of this article is to present the new knowledge obtained from studying two viral campaigns that took place in a virtual world which followed the branching process. The results show that it is possible to reduce the time needed to estimate the model parameters of the campaign and, moreover, some important aspects of time-generations relationship are presented.Comment: In proceedings of the 4th International Conference on Social Informatics, SocInfo 201

Some results and problems for anisotropic random walks on the plane

This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the properties of this random walk concerning strong approximations, local times and range. We give a survey of these results together with some further problems.Comment: 20 page

An asymptotic representation for products of random matrices

AbstractLet {Xk} be a stationary ergodic sequence of nonnegative matrices. It is shown in this paper that, under mild additional conditions, the logarithm of the i, jth element of Xt···X1 is well approximated by a sum of t random variables from a stationary ergodic sequence. This representation is very useful for the study of limit behaviour of products of random matrices. An iterated logarithm result and an estimation result of use in the theory of demographic population projections are derived as corollaries