Elementary congestion models sometimes require analysis of G/G/l systems with hypere.xponentially distributed interarrival time and service time distributions. It is shown that for such systems, the ergodic waiting time distribution is itself hypere.xponentially distributed. A simple computational procedure is provided to fmd the parameters needed. Green's function methods are employed to motiv...

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x1 using the entropy of the k-block empirical probability and letting k grow with n roughly like logn. We further assume that the distribution of the process is a g-measure with respect to a continuous and regular g-function. We prove large deviation principles for conditional, non-conditional an...

We study the centraliser of locally compact group extensions of er-godic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group extensions are constructed. Smooth versions of some of the constructions are also given. §0 Introduction Let T be an ergodic probability preserving transfor...

this paper provides a review on major ergodic features of semi-independent hyper mv {algebra dynamical systems. theorems are presentedto make contribution to calculate the entropy. particularly, it is proved that thetotal entropy of those semi-independent hyper mv {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

Let g be a function which assigns to each stationary process (Xn) ∞ n=1 and to each sample X1 . . . Xn of the process a real number g(X1, . . . , Xn), which may also depend on the distribution of (Xn). We obtain effective bounds on the probability that the sequence (g(X1, . . . , Xn)) ∞ n=1 crosses a fixed interval some number of times in terms of a quantity measuring the “average sub-additivit...

For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ on the probability space such that the 1’st cohomology group of σΛ, H (σΛ), is equal to Char(G)×Λ. We deduce that G has un...

X f dm, provided the action is ergodic. The main tool used in the proof of this result is Wiener’s maximal inequality, which asserts that the maximal function f ∗ β (x)= supt>0 |π(βt )f (x)| satisfies m{x : f ∗ β (x)≥ δ} ≤ (C/δ)‖f ‖L1(X). Consider the following generalization of the foregoing setup. LetG be a connected Lie group G, and let K be a compact subgroup. Assume there exists a G-invari...

Let (St)t be a k-state Markov chain with ergodic transition probability matrix (t.p.m.) Γ = (γi,j)i,j=1,...,k having the stationary distribution π = (π1, . . . , πk). In the following we always assume πj > 0 for j = 1, . . . , k. For a (disjoint) partition G = {G1, . . . , Gr} of the state space (into non-empty sets), we let G(j) be the function which maps a state j ∈ {1, . . . , k} onto its gr...

We investigate the connection between the abelian rank of a countable amenable group and the existence of good averaging sequences (eg for the ergodic theorem). We show that if G is a group with finite abelian rank r(G), then 2 is a lower bound on the constant associated to a Tempel’man sequence, and if G is abelain there is a Tempel’man sequence in G with this constant. On the other hand, infi...

We study some self-interacting diffusions living on R solutions to: dXt = dBt − g(t)∇V (Xt − μt)dt where μt is the empirical mean of the process X , V is an asymptotically strictly convex potential and g is a given function, not increasing too fast to the infinity or constant. The authors have already proved that the ergodic behavior of X is strongly related to g. We go further and, using the s...