Concentration of measure and logarithmic Sobolev inequalities
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.
Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the asymptotic behavior of the survival probability. Next the size of the population and the shape of the random environment...
In this paper we study finite state conditional Markov chains (CMCs). We give two examples of CMCs, one which admits intensity, and another one, which does not admit an intensity. We also give a sufficient condition under which a doubly stochastic Markov chain is a CMC. In addition we provide a method for construction of conditional Markov chains via change of measure.