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.

Involvement in environmental causes, does the joint effect between subjective income and the performance of the country matter?

Previous research has shown that richer people are more likely to engage in an environmentalcause. We extend it by considering the joint effect between subjective income and a set of macroeconomicvariables. For doing so, we employ the fifth wave of the World Values Survey (WVS).This study provides clear evidence that even when both factors matter, people´s attitudes cruciallydepend on the interaction effect. Hence, those measures that affect the characteristics of thecountry would also change the disposition to be involved.