Convergence of switching diffusions

This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on semimartingale techniques, so that no Markovian assumption for the modulating process is needed

Basic Characteristics of Photography Courses in Washington State High Schools

The purposes of this study were (1) to determine whether photography is being taught as a high school class; (2) to determine the factors which influence the offering of such a class; and (3) to discover the characteristics of such a class when offered

On the non-integrability of the Popowicz peakon system

We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation with Painlev\'e analysis provides strong evidence that the Popowicz system is non-integrable. Nevertheless, we are able to construct exact travelling wave solutions in terms of an elliptic integral, together with a degenerate travelling wave corresponding to a single peakon. We also describe the dynamics of N-peakon solutions, which is given in terms of an Hamiltonian system on a phase space of dimension 3N.Comment: 8 pages, AIMS class file. Proceedings of AIMS conference on Dynamical Systems, Differential Equations and Applications, Arlington, Texas, 200

A note on arbitrage under transaction costs

Guasoni (2006) introduced a simple condition for the absence of arbitrage opportunities. In this note we show that his results remain valid under a weaker notion of arbitrage which arises by excluding liquidation costs from the value process of a portfolio