Related papers: Ergodic Theorems for Lower Probabilities
General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this letter, we introduce a systematic method to construct a series of entropies,…
We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…
The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these…
The trivial proof of the ergodic theorem for a finite set $Y$ and a permutation $T:Y\to Y$ shows that for an arbitrary function $f:Y\to{\mathbb R}$ the sequence of ergodic means $A_n(f,T)$ stabilizes for $n \gg |T|$. We show that if $|Y|$…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
We prove pointwise and maximal ergodic theorems for probability measure preserving (p.m.p.) actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type $III_1$. We show that this…
This article shortly provides related proofs of the ergodic theorems of von Neumann, Birkhoff, Wiener, and Rokhlin's lemma for $Z^d$-actions with an invariant measure. It is shown how some deviations of ergodic averages can be structured.…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs.…
We give a short combinatorial proof of the classical pointwise ergodic theorem for probability measure preserving $\mathbb{Z}$-actions. Our approach reduces the theorem to a tiling problem: tightly tile each orbit by intervals with desired…
A rather general ergodic type scheme is presented on arbitrary sets X, as they are generated by arbitrary mappings T : X \longrightarrow X. The structures considered on X are given by suitable subsets of the set of all of its finite…
In this work we prove the pointwise ergodic theorem for harmonic degree 1 cocycle of a measurable stationary action of Z^d on a probability space. In a precedent paper Boivin and Derriennic (1991) studied this theorem for not necessarily…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
The aim of this paper is to prove ergodic decomposition theorems for probability measures quasi-invariant under Borel actions of inductively compact groups (Theorem 1) as well as for sigma-finite invariant measures (Corollary 1). For…
The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a…
Here we briefly discuss how negative numbers, or "negative probabilities", can naturally arise in probabilistic expressions and be given an operational interpretation. Like the use of negative numbers in arithmetical expressions, the use of…
The idea of writing a table of probabilistic data for a quantum or classical system, and of decomposing this table in a compact way, leads to a shortcut for Hardy's formalism, and gives new perspectives on foundational issues.