Related papers: Ergodic Theorems for Lower Probabilities
We prove a multidimensional ergodic theorem with weighted averages for the action of the group $\mathbb{Z}^d$ on a probability space. At level $n$ weights are of the form $n^{-d} \psi(j/n)$, $ j\in \mathbb{Z}^d$, for real functions $\psi$…
A short proof of the classic Hardy inequality is presented for $p$-norms with $p>1$. Along the lines of this proof a sharpened version is proved of a recent generalization of Hardy's inequality in the terminology of probability theory. A…
We apply the methods of ergodic theory to both simplify and significantly extend some classical results due to Stewart, Tijdeman, and Ruzsa. One of the notable features of our approach is the utilization of pointwise ergodic theory.
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…
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…
Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that…
The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…
It is a well known general principle that the Fourier transform of a random measure is small, except at the zero frequency, in various senses for appropriate notions of randomness. In this note we develop analogues of this principle for two…
We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…
We obtain ergodic theorems for multiple iterated sums and integrals of the form $\Sigma^{(\nu)}(t)=\sum_{0\leq k_1<...<k_\nu\leq t}\xi(k_1)\otimes\cdots\otimes\xi(k_\nu)$, $t\in[0,T]$ and $\Sigma^{(\nu)}(t)=\int_{0\leq s_1\leq...\leq…
The objective of this paper is to characterize the structure of the set $\Theta$ for a continuous ergodic upper probability $\mathbb{V}=\sup_{P\in\Theta}P$ (Theorem \ref {main result}): . $\Theta$ contains a finite number of ergodic…
Recently, T. Tao gave a finitary proof a convergence theorem for multiple averages with several commuting transformations and soon later, T. Austin gave an ergodic proof of the same result. Although we give here one more proof of the same…
We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the…
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.