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Mean field limit for the one dimensional Vlasov-Poisson equation

Maxime Hauray (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

We consider systems of N particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the Vlasov-Poisson equation. Actually a rigorous proof of that convergence was given by Trocheris in [Tro86]. Here we shall give a simpler proof of this result, and explain why it implies the so-called “Propagation of molecular chaos”. More precisely, both results will...

Medidas de incertidumbre asociadas a J-divergencias.

Miquel Salicrú Pages, Miquel Calvo Llorca (1988)

Trabajos de Estadística

En este trabajo se presenta la familia de medidas de incertidumbre asociadas a J-divergencias, que resultan de la distancia entre una distribución y la distribución en la que todos los procesos son equiprobables. Se estudian propiedades teóricas de la familia atendiendo a la pérdida de incertidumbre, a la concavidad y a la condición de medida decisiva. Finalmente se compara a nivel muestral la medida de incertidumbre definida por la función φ(t) = -t log t con las medidas de entropía comúnmente...

Minimum variance importance sampling via Population Monte Carlo

R. Douc, A. Guillin, J.-M. Marin, C. P. Robert (2007)

ESAIM: Probability and Statistics

Variance reduction has always been a central issue in Monte Carlo experiments. Population Monte Carlo can be used to this effect, in that a mixture of importance functions, called a D-kernel, can be iteratively optimized to achieve the minimum asymptotic variance for a function of interest among all possible mixtures. The implementation of this iterative scheme is illustrated for the computation of the price of a European option in the Cox-Ingersoll-Ross model. A Central Limit theorem as well...

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...

Multivariate multiple comparisons with a control in elliptical populations

Naoya Okamoto, Takashi Seo (2013)

Discussiones Mathematicae Probability and Statistics

The approximate upper percentile of Hotelling's T²-type statistic is derived in order to construct simultaneous confidence intervals for comparisons with a control under elliptical populations with unequal sample sizes. Accuracy and conservativeness of Bonferroni approximations are evaluated via a Monte Carlo simulation study. Finally, we explain the real data analysis using procedures derived in this paper.

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