Geodesic
Inequalities for the total variation between the
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 653-660

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Let $\xi=(\xi_k)_{k\in\mathbf{N}^*}$ be a stationary homogeneous Markov chain and its translate $\xi+a=(\xi_k+a_k)_{k\in\mathbf{N}^*}$ be a real sequence. We prove an inequality for the total variation between the distributions of $\xi$ and $\xi+a$. This result allows us to give sufficient conditions for absolute continuity of these distributions. Next, we consider $\xi=(\xi_k)_{k\in\mathbf{N}^*}$ a sequence of independent and identically distributed random variables and another sequence of independent variables $\eta=(\eta_k)_{k\in\mathbf{N}^*}$, which is independent of $\xi$. We estimate the total variation between the distributions of $\xi$ and $\xi+\eta$ and apply the obtained results to the problem of absolute continuity.
Keywords: random translation, absolute continuity.
Mots-clés : total variation, Markov chain 
@article{TVP_1999_44_3_a11,
     author = {C. Noquet},
     title = {Inequalities for the total variation between the},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {653--660},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a11/}
}
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C. Noquet. Inequalities for the total variation between the. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 653-660. http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a11/