Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Direct MR arthrography at 1.5 and 3.0 T: signal dependence on gadolinium and iodine concentrations--phantom study

PURPOSE: To prospectively quantify in vitro the influence of gadopentetate dimeglumine and ioversol on the magnetic resonance (MR) imaging signal observed with a variety of musculoskeletal pulse sequences to predict optimum gadolinium concentrations for direct MR arthrography at 1.5 and 3.0 T. MATERIALS AND METHODS: In an in vitro study, T1 and T2 relaxation times of three dilution series of gadopentetate dimeglumine (concentration, 0-20.0 mmol gadolinium per liter) at ioversol concentrations with iodine concentration of 0, 236.4, and 1182 mmol iodine per liter (corresponding to 0, 30, and 150 mg of iodine per milliliter) were measured at 1.5 and 3.0 T. The relaxation rate dependence on concentrations of gadolinium and iodine was analytically modeled, and continuous profiles of signal versus gadolinium concentration were calculated for 10 pulse sequences used in current musculoskeletal imaging. After fitting to experimental discrete profiles, maximum signal-to-noise ratio (SNR), gadolinium concentration with maximum SNR, and range of gadolinium concentration with 90% of maximum SNR were derived. The overall influence of field strength and iodine concentration on these parameters was assessed by using t tests. The deviation of simulated from experimental signal-response profiles was assessed with the autocorrelation of the residuals. RESULTS: The model reproduced relaxation rates of 0.37-38.24 sec(-1), with a mean error of 4.5%. Calculated SNR profiles matched the discrete experimental profiles, with autocorrelation of the residuals divided by the mean of less than 5.0. Admixture of ioversol consistently reduced T1 and T2, narrowed optimum gadolinium concentration ranges (P = .004-.006), and reduced maximum SNR (P < .001 to not significant). Optimum gadolinium concentration was 0.7-3.4 mmol/L at both field strengths. At 3.0 T, maximum SNR was up to 75% higher than at 1.5 T. CONCLUSION: Admixture of ioversol to gadopentetate dimeglumine solutions results in a consistent additional relaxation enhancement, which can be analytically modeled to allow a near-quantitative a priori optimized match of contrast media concentrations and imaging protocol for a broad variety of pulse sequences.

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.