In this paper we study ergodic measures on non-simple Bratteli diagrams of finite rank that are invariant with respect to the cofinal equivalence relation. We describe the structure of finite rank diagrams and prove that every ergodic invariant measure (finite or infinite) is an extension of a finite ergodic measure defined on a simple subdiagram. We find some algebraic criteria in terms of ent...

This paper discusses the difference between ergodic and non-ergodic texts by considering the different levels of reasoning required of an agent in each case. The difference indentified between such texts is based on the distinction between credal and pignistic reasoning in the transferable belief model. It is argued that non-ergodic texts require an active agent to reason about the state of the...

In 1931, Birkhoff gave a general and rigorous description of the ergodic hypothesis from statistical meachanics. This concept can be generalized by group actions of a large class of amenable groups on σ-finite measure spaces. The expansion of this theory culminated in Lindenstrauss’ celebrated proof of the general pointwise ergodic theorem in 2001. The talk is devoted to the introduction of abs...

We study a new class of ergodic backward stochastic differential equations (EBSDEs for short) which is linked with semi-linear Neumann type boundary value problems related to ergodic phenomenas. The particularity of these problems is that the ergodic constant appears in Neumann boundary conditions. We study the existence and uniqueness of solutions to EBSDEs and the link with partial differenti...

Proof-theoretic aspects of obtaining a constructive version of the mean ergodic theorem – p. 1/27 Introduction 'Proof mining' is the subfield of mathematical logic that is concerned with the extraction of additional information from proofs in mathematics and computer science. G. Kreisel: What more do we know if we have proved a theorem by restricted means other than if we merely know the theore...

If G is a Polish group and Γ is a countable group, denote byHom(Γ,G) the space of all homomorphisms Γ → G. We study properties of the group π(Γ) for the generic π ∈ Hom(Γ,G), when Γ is abelian and G is one of the following three groups: the unitary group of an infinite-dimensional Hilbert space, the automorphism group of a standard probability space, and the isometry group of the Urysohn metric...

We show that Chacon's nonsingular type III transformation T , 0 < 1, is power weakly mixing, i.e., for all sequences of nonzero integers fk1; : : : ; krg, T k1 : : : T kr is ergodic. We then show that in in nite measure, this condition is not implied by in nite ergodic index (having all nite Cartesian products ergodic), and that in nite ergodic index does not imply 2-recurrence.

In this paper we study statistical properties of hyperbolic maps. In particular, we estimate how sums of functions along orbits are distributed relative to intervals which shrink in size. 0. Introduction In this article we shall study statistical properties for the orbits of dynamical systems. Given any measurable map T : X → X and ergodic probabilty measure m we can consider an integrable func...

Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X . Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times λn along which we will be able to estimate the conditional probability P (Xλn+1 = x|X0, . . . , Xλn) from data segment (X0, . . . , Xλn) in a pointwise consistent way for a restricted ...