Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.

Conducta instrumental del chimpace (Pan troglodytes) en su habitat natural

La constatación del uso sistemático de instrumentos por los chimpancés en su habitat natural ha planteado el problema de la aplicación del término cultura a un primate no humano. Una de las características de la cultura es la aparición de variantes conductuales en grupos separados. El propósito de este trabajo es revisar, con los datos disponibles en la actualidad, la hipótesis formulada por Sabater Pi (1974b) de que existen tres zonas culturales en los chimpancés e intentar identificar el origen ecológico y/o social de estas diferencias.