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Condiciones de martingala sobre un proceso de aprendizaje tipo beta con dos operadores y reforzamiento no contingente simple. 2. Caso general.

Juan Ignacio Domínguez Martínez (1985)

Trabajos de Estadística e Investigación Operativa

Se analizan las condiciones bajo las cuales un modelo de aprendizaje no lineal (modelo beta) con dos operadores y reforzamiento no contingente simple es una sub(super)martingala en el supuesto de que todas las respuestas sean reforzadas, generalizándose al caso de ausencia de reforzamiento.Las condiciones establecidas, que nos conducen a 23 casos posibles, permiten analizar exhaustivamente el comportamiento asintótico del modelo y compararlo con la clasificación de Norman.

Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations

Jens Christian Claussen (2008)

Banach Center Publications

Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit N → ∞ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in 1/√N. Consequences and relations to some previous approaches...

Drift, draft and structure: some mathematical models of evolution

Alison M. Etheridge (2008)

Banach Center Publications

Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to classical...

Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVille, C. S. Peskin, J. H. Spencer (2010)

Mathematical Modelling of Natural Phenomena

We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...

Economic assessment of the Champagne wine qualitative stock mecanism

Jacques Laye, Maximilien Laye (2006)

RAIRO - Operations Research

In the wine AOC system, the regulation of quantities performed by the professional organizations is aimed to smooth the variations of the quality of the wine due to the variations in the climate that affect the quality of the grapes. Nevertheless, this regulation could be damaging to the consumers due to the price increase resulting from the reduction of the quantities sold on the market. We propose a stochastic control model and a simulation tool able to measure the effects of this mechanism...

Macroscopic non-uniqueness and transversal fluctuation in optimal random sequence alignment

Saba Amsalu, Heinrich Matzinger, Serguei Popov (2007)

ESAIM: Probability and Statistics

We investigate the optimal alignment of two independent random sequences of length n. We provide a polynomial lower bound for the probability of the optimal alignment to be macroscopically non-unique. We furthermore establish a connection between the transversal fluctuation and macroscopic non-uniqueness.

Markov operators acting on Polish spaces

Tomasz Szarek (1997)

Annales Polonici Mathematici

We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.

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