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),...

We derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte Carlo simulation. We show that the subdiffusive fractional equations with constant anomalous exponent μ in a bounded domain [0,L] are not structurally stable with respect to the nonhomogeneous variations of paramet...

We give a method for obtaining radially symmetric solutions for the critical exponent problem ?u + a(x)u = u q + u 2 ?1 in R N u > 0 and R R N jruj 2 < 1 where, outside a ball centered at the origin, the non-negative function a is bounded from below by a positive constant ao > 0. We remark that, diierently from the literature, we do not require any conditions on a at innnity.

This paper describes, in detail, techniques for measuring the Hurst parameter. Measurements are given on artificial data both in a raw form and corrupted in various ways to check the robustness of the tools in question. Measurements are also given on real data, both new data sets and well-studied data sets. All data and tools used are freely available for download along with simple “recipes” wh...

A one-dimensional tight-binding Hamiltonian describes the evolution of a single impurity interacting locally with N electrons. The impurity spectral function has a power-law singularity A(ω) ∝| ω− ω0 |−1+β with the same exponent β that characterizes the logarithmic decay of the quasiparticle weight Z with the number of electrons N , Z ∝ N−β. The exponent β is computed by (1) perturbation theory...

We study the asymptotic expansions with respect to h of