### A central limit theorem for non stationary mixing processes

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A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit test. We also...

The paper is devoted to the study of stationary random sequences. A concept of dual sequences is discussed. The main aim of the paper is to establish a relationship between the errors of linear least squares predictions for sequences and their duals.

We construct a large family of ergodic non-Markovian processes with infinite memory having the same p-dimensional marginal laws of an arbitrary ergodic Markov chain or projection of Markov chains. Some of their spectral and mixing properties are given. We show that the Chapman-Kolmogorov equation for the ergodic transition matrix is generically satisfied by infinite memory processes.

We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.

Let $\left\{{X}_{n}\right\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set $\mathcal{X}$ and that $f\left(X\right)$ is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times ${\lambda}_{n}$ along which we will be able to estimate the conditional expectation $E\left(f\left({X}_{{\lambda}_{n}+1}\right)\right|{X}_{0},\cdots ,{X}_{{\lambda}_{n}})$ from the observations $({X}_{0},\cdots ,{X}_{{\lambda}_{n}})$ in a point wise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series...

We present a stochastic model which yields a stationary Markov process whose invariant distribution is maximum stable with respect to the geometrically distributed sample size. In particular, we obtain the autoregressive Pareto processes and the autoregressive logistic processes introduced earlier by Yeh et al

The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.