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This paper gives an approximation of the solution of the Boltzmann
equation by stochastic interacting particle systems in a case of
cut-off collision operator and small initial data. In this case,
following the ideas of Mischler and Perthame, we prove the existence
and uniqueness of the solution of this equation and also the existence
and uniqueness of the solution of the associated nonlinear martingale
problem.
Then, we first delocalize the interaction by considering a mollified
Boltzmann...
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE method...
The aim of this paper is to take an in-depth look at the long
time behaviour of some continuous time Markovian dynamical systems and at its
numerical analysis. We first propose a short overview of the main
ergodicity properties
of time continuous homogeneous Markov processes (stability, positive
recurrence). The basic
tool is a Lyapunov function. Then, we investigate if these
properties still hold for
the time discretization of these processes, either with constant or
decreasing step (ODE...
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