Stochastic bounds for Levy processes

Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Levy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Levy processes which converge to \infty in probability.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000031

Overshoots and undershoots of L\'{e}vy processes

We obtain a new fluctuation identity for a general L\'{e}vy process giving a quintuple law describing the time of first passage, the time of the last maximum before first passage, the overshoot, the undershoot and the undershoot of the last maximum. With the help of this identity, we revisit the results of Kl\"{u}ppelberg, Kyprianou and Maller [Ann. Appl. Probab. 14 (2004) 1766--1801] concerning asymptotic overshoot distribution of a particular class of L\'{e}vy processes with semi-heavy tails and refine some of their main conclusions. In particular, we explain how different types of first passage contribute to the form of the asymptotic overshoot distribution established in the aforementioned paper. Applications in insurance mathematics are noted with emphasis on the case that the underlying L\'{e}vy process is spectrally one sided.Comment: Published at http://dx.doi.org/10.1214/105051605000000647 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Perturbed and non-perturbed brownian taboo processes

ABSTRACT. – In this paper we study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the α-perturbed Brownian taboo process, which is an analogous version of an α-perturbed Brownian motion.We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and lower functions of the supremum as t →∞. In the Brownian case these include extensions of recent results in Lambert [4], but are proved in a quite different way. 2001 Éditions scientifiques et médicales Elsevier SAS AMS classification: 60K05; 60J15 RÉSUMÉ. – Dans cet article, nous étudions le processus Brownien tabou qui est une version du mouvement Brownien, conditionné à rester dans un intervalle fini, et le processus Brownien tabou α-perturbé qui est une version semblable du mouvement Brownien α-perturbé. Nous sommes particulièrement intéressés par le comportement asymptotique du supremum du processus tabou et nos principaux résultats fournissent des intégrales tests pour des fonctions majorantes et minorantes du supremum lorsque t → ∞. Dans le cas Brownien, ces résultats incluent des extensions de résultats récents de Lambert [4], mais ceux-ci sont prouvés de maníère différente. 2001 Éditions scientifiques et médicales Elsevier SAS 1

On a Fluctuation Identity for Random Walks and Lévy Processes

In this paper, some identities in laws involving ladder processes for random walks and Lévy processes are extended and unified. 2000 Mathematics Subject Classification 60G50, 60G51 (primary), 60G17 (secondary

Exploring the ontological dimension of dialogic education through an evaluation of the impact of Internet mediated dialogue across cultural difference

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.It has been claimed that dialogic education implies a direction of change upon an ontological dimension from monologic closed identities in the direction of more dialogic identifications characterised by greater openness to the other and greater identification with the process of dialogue. This paper recapitulates that theory and then provides an empirical illustration of what it looks like in practice. In order to do this a methodology for researching the impact of dialogic education is outlined and applied to the evaluation of the impact of a programme designed to promote greater dialogic open-mindedness: the Tony Blair Institute for Global Change’s Generation Global Project (GG) supports schools in over twenty different countries to engage in dialogue with each other through videos and blogs. The methodology put forward argues that the understanding sought by educational research is dialogic in that it emerges from the dialogue between inside and outside perspectives. The findings offer some clear evidence of a shift in identifications resulting from dialogue through the analysis of changes in online language use supported by interview evidence. This study suggests that a pedagogical intervention can produce identity change in the direction of becoming more dialogic and shows that it is possible to evaluate this change.The empirical aspect of this paper reports on research funded by the Tony Blair Institute for Global Change