We derive upper and lower bounds on the reliability function for the common-message discrete memoryless broadcast channel with variable-length feedback. We show that the bounds are tight when the broadcast channel is stochastically degraded. For the achievability part, we adapt Yamamoto and Itoh’s coding scheme by controlling the expectation of the maximum of a set of stopping times. For the co...

This paper presents evidence of long-range dependence in bid–ask prices for individual equity prices in the Brazilian stock market. Moreover, using the Hurst exponent calculated by the Local Whittle method as a measure of long-range dependence, we find evidence supporting that bid–ask prices shows a stronger long-range dependence than the one usually found in closing and opening prices. Finally...

Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. Recent empirical studies of stock market indices examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Lévy-stable distribution L(alpha)(r) with some index 0<alpha< or =2. While the Lévy distribution cannot be expressed in a cl...

Classical site percolation was used to study numerically the effect of interplane coupling in the range 10(-1)-10(-6) of the in-plane coupling on the static correlation length exponent nu and the critical dimension D. It was found that even for the smallest coupling values the exponents take their three-dimensional (3D) values for sufficiently large system sizes. The percolation threshold p(c),...

A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction...

We show that the probability, P0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P0(l) approximately l(theta). Here straight theta is a "spatial" persistence exponent, and takes different values, straight theta(s) or straight theta(0), depending on ho...

Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single paramete...