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Local limit theorems on some non unimodular groups.

Emile Le PageMarc Peigné — 1999

Revista Matemática Iberoamericana

Let Gd be the semi-direct product of R*+ and Rd, d ≥ 1 and let us consider the product group Gd,N = Gd x RN, N ≥ 1. For a large class of probability measures μ on Gd,N, one prove that there exists ρ(μ) ∈ ]0,1] such that the sequence of finite measures {(n(N+3)/2 / ρ(μ)n) μ*n}...

On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains

Ion GramaÉmile Le PageMarc Peigné — 2014

Colloquium Mathematicae

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed mixing...

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