from which, dividing through by N, and letting N -a, we will get X(h) . a(h) en(h) e. Now letting e -O 0, the proof is complete. The proof of (E) reproduces the combinatorial essence of G. D. Birkhoff's proof of the Strong Ergodic Theorem.2 We rely on the fact that the "components" of h form a Boolean algebra, and may be treated like sets. 1 L. Kantorovitch. "Lineare halbgeordnete Raume," Math....

Let σ(u), u ∈ R be an ergodic stationary Markov chain, taking a finite number of values a1, . . . , am, and b(u) = g(σ(u)), where g is a bounded and measurable function. We consider the diffusion type process dX t = b(X ε t /ε)dt+ ε σ `

In this paper we use infinite ergodic theory to study limit sets of essentially free Kleinian groups which may have parabolic elements of arbitrary rank. By adapting a method of Adler, we construct a section map S for the geodesic flow on the associated hyperbolic manifold. We then show that this map has the Markov property and that it is conservative and ergodic with respect to the invariant m...

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Let S be an abelian group of automorphisms of a probability space (X,A, μ) with a finite system of generators (A1, ..., Ad). Let A l denote A1 1 ...A ld d , for l = (l1, ..., ld). If (Zk) is a random walk on Z , one can study the asymptotic distribution of the sums ∑n−1 k=0 f ◦AZk(ω) and ∑ l∈Z P(Zn = l)A f , for a function f on X . In particular, given a random walk on commuting matrices in SL(...

For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a “universal” hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of G.

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

The ergodic capacity of underlay cognitive (secondary) dual-hop relaying systems is analytically investigated. Specifically, the amplify-and-forward transmission protocol is considered, while the received signals undergo multipath fading and shadowing with non-identical statistics. To efficiently describe this composite type of fading, the well-known generalized-K fading model is used. New anal...

J. George Shanthikumar University of California Berkeley Ushio Sumita University of Rochester (Received September 25,1985: Revised March 27,1986) We consider a single server queueing system G/G/l having general interarrival times (not necessarily i.i.d), i.i.d. service times, and LIFO-P (preemptive last in first out, but not restricted to resumption) service disciplines. Furthermore a customer ...

We introduce a natural equivalence relation on the space H0 of horofunctions of a word hyperbolic group that take the value 0 at the identity. We show that there are only finitely many ergodic measures that are invariant under this relation. This can be viewed as a discrete analog of the Bowen-Marcus theorem. Furthermore, if η is such a measure and G acts on a space (X,μ) by p.m.p. transformati...