We establish conditional limit theorems, pointwise in the initial state, for absorbing Markov chains on a compact metric space $M$. We assume $L^1(M,\rho)$-continuous transition densities, irreducibility and aperiodicity. For the observable $f_\beta(x)=d_M(x,x_0)^{-\beta}$, with suitable $x_0$ satisfying $\rho(B_r(x_0)...
Bernat Bassols Cornudella, Matheus M. Castro· 1 citation
We show that finite-order exponential mixing does not imply the central limit theorem for smooth diffeomorphisms. For every integer $R\geq2$, we construct a $\mathcal{C}^{\infty}$ diffeomorphism $T:M\to M$ of a compact smooth manifold $M$ and a $T$-invariant probability measure $\mu$ such that $(T,\mu)$ is exponentiall...
Bernat Bassols Cornudella, Matheus M. Castro· 0 citations
We establish conditional limit theorems, pointwise in the initial state, for absorbing Markov chains on a compact metric space $M$. We assume $L^1(M,\rho)$-continuous transition densities, irreducibility and aperiodicity. For the observable $f_\beta(x)=d_M(x,x_0)^{-\beta}$, with suitable $x_0$ satisfying $\rho(B_r(x_0)...
Bernat Bassols Cornudella, Matheus M. Castro· 0 citations
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