Non-parametric Estimation of Stochastic Differential Equations with Sparse Gaussian Processes

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a non-parametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudo-samples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behaviour of complex systems

Una economía política para el sistema rural en Galicia

[Resumen] El campo en Galicia está al final de una larga etapa de transición. Se asiste a la transformación de un sistema agrícola total, que era el existente hace décadas en nuestro agro y que informaba cultural y económicamente toda una forma o modo de vida, a un nuevo sistema rural. En Galicia coexisten hoy comarcas en muy distinto estadio económico, desde las más avanzadas, donde la actividad agraria tiene ya una pequeña incidencia en la economía, a las más deprimidas, todavía con agricultura de autoconsumo y con alta dependencia de las transferencias de rentas para su subsistencia. En cualquier caso, en el conjunto comienzan a surgir los esquemas organizativos y la diferenciación social que caracterizan a los países más modernos.[Abstract] The countryside in Galicia is at the end of a long transition period. We are attending a complete agricultural system transformation, which was the one that existed decades ago in our farmalands and that informed us culturally and ecomomically of a way of life, to a new rural system. Nowadays in Galicia, two regions in very different economic states coexist, from the most advanced, where the agricultural activity already has a little impact on the economy, to the most depressed, with subsistance agriculture and highly dependent on rent transfers to survive. In any case, as a group, the organizational diagrams and the social differentation that define the most modern countries, have started to appear