A new class of interacting Markov chain Monte Carlo methods
We present a new class of interacting Markov chain Monte Carlo methods to approximate numerically discrete-time nonlinear measure-valued equations. These stochastic processes belong to the class of self-interacting Markov chains with respect to their occupation measures. We provide several convergen...
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| Format: | Journal article |
| Jezik: | English |
| Izdano: |
2010
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| Izvleček: | We present a new class of interacting Markov chain Monte Carlo methods to approximate numerically discrete-time nonlinear measure-valued equations. These stochastic processes belong to the class of self-interacting Markov chains with respect to their occupation measures. We provide several convergence results for these new methods including exponential estimates and a uniform convergence theorem with respect to the time parameter, yielding what seems to be the first results of this kind for this type of self-interacting models. We illustrate these models in the context of Feynman-Kac distribution semigroups arising in physics, biology and in statistics. © 2009 Académie des sciences. |
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