Other Research Projects
Title: Stochastic calculus with applications to Social Sciencies
We study the following issues
A) Application of the United Nations Precautionary Approach for the implementation of sustainable policies of exploitation of depleted fisheries
B) Data analysis of a weak chaotic component corrupted by large observational noise (up to 300% noise/signal ratio) , with the objective of separating the deterministic component
C) Central problems of Fractal Geometry on self-similar sets, as the determination of the exact value of Hausdorff type mesures (nonoverlapping case) or dimension of these measures (overlapping case). Objective: Selection of the most suitable measures and computable algorithms to obtain their values and dimensions
D) An original application of mathematics to Psichology for the study of the long run stability of sentimental relationships beween human couples, with the aim of founding a mathematical setting for such analysis
Title: Nonlinear stochastic equilibria. economic and environmental applications
We analyse the properties of the stationary probability distributions arising in four mathematical issues of interest in Economics and Environmental Sciences:
a) Long term forecasting of chaotic time series corrupted by observational noise.
b) Geometry of probability distribution on fractal media.
c) Labour market, inmigratory flow and technological innovation.
d) Optimal exploitation of renewable resources. The problem of extinction in presence of increasing marginal returns.
Title: Dynamics and geometry of stochastic equilibria
We analyse the properties of the stationary probability distributions in the framework of random dynamical systems. The objectives detailed below concern five relevant fields in operations research with applications in economics and natural sciences:
a)Characterization of the deterministic kernel and stochastic component in large time series, with application in controlled experiments and financial markets.
b)Stochastic dynamical optimisation models in presence of increasing marginal returns, with application to economic growth and optimal exploitation of renewable resources.
c)Relationships between the skill distribution, wages, vacancies, unemployment and technological innovation in the labour market.
d)Entropy analysis for the measurement of geoeconomic inequality and efficiency of the distribution and association of resources, with special concern for the relative distribution sanitary services/demography.
e)Determination of the stationary distribution of the total number of arrivals and waiting individuals in queue systems with repeated attemps.
Title : Separation of deterministic components in time series
We propose the construction of algorithms devised for the detection and separation of medium power determinist components in large time series.
We intend to apply these algorithms to the analysis of money exchange rates and financial markets. Some practical and theoretical consequences of this analysis will be explored in the setting of the endogenous dynamics with complex behaviour as a model for the economic cycle.
Title: Analysis of spatial correlations in time series.
Director: Manuel Morán
Participants: M.E. Mera, M. Moran and J.M. King
Duration :1997-2000
Financing entity: Ministry of Education and Culture
Title: Nonlinear analysis of time series. Application to Financial Markets.
Director: Manuel Morán
Participants: M.E. Mera, M. Moran and J.M. King
Duration: 1994-1997
Financing entity: Ministry of Education and Culture
Title: Chaos Detection in the ocean tides.
Director: Manuel Morán
Participants: M.E. Mera, M. Moran and J.M. King
Duration: 1992-1994
Funding body: Climate Maritime Program (Port of Spain).
