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An introduction to probabilistic methods with applications

Pierre Del MoralNicolas G. Hadjiconstantinou — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

This special volume of the ESAIM Journal, , contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics. In this preface, we provide a brief presentation...

Low-variance direct Monte Carlo simulations using importance weights

Husain A. Al-MohssenNicolas G. Hadjiconstantinou — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We present an efficient approach for reducing the statistical uncertainty associated with direct Monte Carlo simulations of the Boltzmann equation. As with previous variance-reduction approaches, the resulting statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the characteristic value of quantity of interest) is small and independent of the magnitude of the deviation from equilibrium, making the simulation of arbitrarily small deviations from equilibrium possible....

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