Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Modelling official and parallel exchange rates in Colombia under alternative regimes: a non-linear approach

We examine the long-run relationship between the parallel and the official exchange rate in Colombia over two regimes; a crawling peg period and a more flexible crawling band one. The short-run adjustment process of the parallel rate is examined both in a linear and a nonlinear context. We find that the change from the crawling peg to the crawling band regime did not affect the long-run relationship between the official and parallel exchange rates, but altered the short-run dynamics. Non-linear adjustment seems appropriate for the first period, mainly due to strict foreign controls that cause distortions in the transition back to equilibrium once disequilibrium occurs