### 0n the Domain Of Attraction of Stable and of Extreme Value Distributions

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We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals “on-the-fly” as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We...

We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics...

A central limit theorem is proved on the space ${\mathcal{P}}_{n}$ of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on ${\mathcal{P}}_{n}$ are defined and investigated. One uses a Taylor expansion of the spherical functions on ${\mathcal{P}}_{n}$.