相关论文: Stationary processes whose filtrations are standar…

Let $X$ be a stationary process with values in some $\sigma$-finite measured state space $(E,\mathcal{E},\pi)$, indexed by ${\mathbb Z}$. Call ${\mathcal F}^X$ its natural filtration. In \cite{ceillierstationary}, sufficient conditions were…

We derive a practical standardness criterion for the filtration generated by a monotonic Markov process. This criterion is applied to show standardness of some adic filtrations.

We consider backward filtrations generated by processes coming from deterministic and probabilistic cellular automata. We prove that these filtrations are standard in the classical sense of Vershik's theory, but we also study them from…

A. Vershik discovered that filtrations indexed by the non-positive integers may have a paradoxical asymptotic behaviour near the time $-\infty$, called non-standardness. For example, two dyadic filtrations with trivial tail $\sigma$-field…

Let $X$ be a stationary process with finite state-space $A$. Bressaud et al. recently provided a sufficient condition for the natural filtration of $X$ to be standard when $A$ has size 2. Their condition involves the conditional laws…

We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration,…

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy…

The notion of a homogeneous standard filtration of $\sigma$-algebras was introduced by the author in 1970. The main theorem asserted that a homogeneous filtration is standard, i.e., generated by a sequence of independent random variables,…

M. Smorodinsky and S. Laurent have initiated the study of the filtrations of split-word processes, in the framework of discrete negative time. For these filtrations, we show that Laurent's sufficient condition for non standardness is also…

We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…

It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form…

Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…

A bound uniform over various loss-classes is given for data generated by stationary and phi-mixing processes, where the mixing time (the time needed to obtain approximate independence) enters the sample complexity only in an additive way.…

Processes controlled by stochastic synthesis and degradation (SSD) are widespread in biology but their reaction kinetics are not well understood. Using methods borrowed from the theory of resetting processes, we determine the first-passage…

Stationary determinantal point processes are proved to be Brillinger mixing. This property is an important step towards asymptotic statistics for these processes. As an important example, a central limit theorem for a wide class of…

Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…

We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale…

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the…

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…

We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that…