相关论文: Distributional limits of positive, ergodic station…

We prove distributional limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from non-integrable observables over certain piecewise…

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 prove distributional limit theorems for random walk adic transformations obtaining ergodic distributional limits of exponential chi squared form.

This paper elucidates the connection between stationary symmetric alpha-stable processes with 0<alpha<2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those…

The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…

We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

We study the partial maxima of stationary \alpha-stable processes. We relate their asymptotic behavior to the ergodic theoretical properties of the flow. We observe a sharp change in the asymptotic behavior of the sequence of partial maxima…

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…

We prove a version of pointwise Ergodic Theorem for non-stationary random dynamical systems. Also, we discuss two specific examples where the result is applicable: non-stationary iterated function systems and non-stationary random matrix…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

We study limit laws for return time processes defined on infinite conservative ergodic measure preserving dynamical systems. Especially for the critical cases with purely atomic limiting distribution we derive distorted processes posessing…

We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as diffusion limits in the asymptotic…

It is argued that a diffusion may be ergodic even though the drift field has unbounded outward-directed parts. The discussion employs stochastic and numerical methods.

It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…

A new negative result for nonparametric distribution estimation of binary ergodic processes is shown. The problem of estimation of distribution with any degree of accuracy is studied. Then it is shown that for any countable class of…

We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for…

In this paper, we construct an infinite stationary Diffusion Limited Aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate proportional to the stationary harmonic measure. We prove that…

The aim of the paper is to study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach based on the use of the axioms of probability theory is used for these purposes. Sufficient…

For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the…