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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...
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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