Stability and other limit laws for exit times of random walks from a strip or a halfplane

We show that the passage time, T^*(r), of a random walk S_n above a horizontal boundary at r (r≥0) is stable (in probability) in the sense that as r→∞ for a deterministic function C(r)>0, if and only if the random walk is relatively stable in the sense that as n→∞ for a deterministic sequence B_n>0. The stability of a passage time is an important ingredient in some proofs in sequential analysis, where it arises during applications of Anscombe's Theorem. We also prove a counterpart for the almost sure stability of T^*(r), which we show is equivalent to E|X|<∞, EX>0. Similarly, counterparts for the exit of the random walk from the strip {|y|≤r} are proved. The conditions arefurther related to the relative stability of the maximal sum and the maximum modulus of the sums. Another result shows that the exit position of the random walk outside the boundaries at ±r drifts to ∞ as r→∞ if and only if the random walk drifts to ∞.     

Variational principles for average exit time moments for diffusions in Euclidean space

Let be a smoothly bounded domain in Euclidean space and let be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from of a particle driven by where the average is taken over all starting points in

     

MRI of thermally denatured blood: methemoglobin formation and relaxation effects

Focal regions of T₁-shortening have been observed in magnetic resonance imaging (MRI)-monitored thermal ablations of perfused tissues. The aims of this study were two-fold: to find evidence for heat-induced conversion of hemoglobin (Hb) to methemoglobin (mHb), and to investigate the effects of heat treatment of in-vitro blood components upon their MR relaxation times. Spectrophotometric studies were performed to confirm the heat-induced formation of methemoglobin. Preparations of whole and fractionated blood, previously submitted to elevated temperatures of 40°C to 80°C, were imaged and the relaxation times were calculated. Optical absorption spectra of samples containing free Hb, heated to 60°C, showed increased light absorption at 630 nm, evident of mHb presence. Short T₁ values in whole blood (1.13 s) and packed red blood cell (0.65 s) compartments, heated at 60°C, compared to their baseline values (1.62 s and 0.83 s, respectively), were attributed to mHb formation. In relation to MRI-guided thermal interventions, these results suggest a possible explanation for observation of hyperintense regions on T₁-weighted images.     

A characterization for mixtures of semi-Markov processes

Mixtures of recurrent semi-Markov processes are characterized through a partial exchangeability condition of the array of successor states and holding times. A stronger invariance condition on the joint law of successor states and holding times leads to mixtures of Markov laws.     

The overload phenomenon in gas chromatography

The usual concepts of the dynamics of an overloaded solute band fail to explain several phenomena such as the typical “leading-tail” shape and retention deviations exhibited by overloaded peaks, and why these defects are more commonly observed in short columns. These and other related deviations from theory can be rationalized by a non-classical approach to the overloading phenomenon.     

Empirical bounds for ruin probabilities

We consider the classical model for an insurance business where the claims occur according to a Poisson process and where the distribution for the cost of each claim fulfills Cramér's tail-condition. Under these conditions Lundberg's constant R is of fundamental importance for ruin calculations.We derive estimates of R, based on an observation of the insurance business and investigate the statistical properties of those estimates. We further derive bounds and confidence intervals for ruin probabilities.     

The Asymptotic Behavior of the Ergodic Measure of a Glauber + Kawasaki model

We consider an interacting particle system given by the Glauber + Kawasaki dynamics. It is known that this process has a reaction diffusion equation as hydrodynamic limit. The ergodicity of this process in the presence of a metastable state (double well potential) was recently proved by S. Brassesco et al. In this Letter we prove that, in the limit, as ε → 0, the expected value of each spin converges to the global minimizer of the potential. We also prove decay of correlations of the ergodic measure.AMS Subject Classification (2000). 60K35 (82C22, 82C31)This work was partially supported by CNPq     

Multiple-detector responses or multiple-retention times: what is more informative for gas chromatography peak identification?

Multiple-separation and -detection are two approaches applied at the identification of analytes in chromatography. Using them depends on the physico-chemical properties and elemental content of the analytes. When physico-chemical properties are similar multiple-separation gives better opportunities for the identification. In this case, the efficiency of the columns is very important. When analytes contain some characteristic groups as--NO2, halogen, or nitrogen atoms then multiple-detection will be more useful. The sensitivity and/or selectivity of the detectors increase reliability of identification significantly.