Let {Xi}i≥1 be independent, identically distributed random vectors in ℤd,d≥1. Let LLn(x)≡ℙ(Sn=x),n≥1,x∈ℤd, be the likelihood function for Sn=∑i=1nXi. For integers j≥2 and n≥1, let an(j)≡∑x∈ℤd(Ln(x))j. We show that if X1-X2 has a nondegenerate aperiodic distribution in ℤd and 𝔼(∥X1∥2)>∞, then limn→∞n(j-1)d∕2an(j)≡a(j,d) exists and 0<a(j,d)<∞. Some extensions and open problems are also outlined.

In this paper, a new calibration method for open-chain robotic arms is developed. By incorporating both prior parameter information and artifact measurement data, and by taking recourse to Bayesian inference methods, not only are the robot kinematic parameters updated but also confidence bounds are computed for all measurement data. In other words, for future measurement data not only the most likely end-effector configuration is estimated but also the uncertainty represented as 95% confidence bounds of that pose is computed. To validate the proposed calibration method, a three degree-of-freedom robotic arm was designed, constructed, and calibrated using both typical regression methods and the proposed calibration method. The results of an extensive set of experiments are presented to gauge the accuracy and utility of the proposed calibration method.

A method is proposed for improving the accuracy and self-consistency of bathymetric maps built using an Autonomous Underwater Vehicle (AUV) to create precise prior maps for Terrain-Aided Navigation (TAN), when the Global Positioning System (GPS) or another precise location method is unavailable. This method consists of front-end and back-end. For the front-end, the AUV predicts the measurement of the bathymetry system through Terrain Elevation Measurement Extrapolation Estimation (TEMEE) and calculates the likelihood function using real measurements. After the final Inertial Navigation System (INS) error is obtained by communicating with sensor nodes, the process enters the back-end. A Terrain Correlation Correction Method (TCCM) and an Improved Terrain Correlation Correction Method (ITCCM) are proposed to solve the gradual distribution of the final INS error to each point on a path, and the accuracy of ITCCM was confirmed experimentally. Finally, a TAN simulation experiment was conducted to prove the importance and necessity of map correction using ITCCM. ITCCM was proven to be an effective and important method for correcting maps built using an AUV.

This paper discusses the use of parametric models for description of the term structure of interest rates and their uses. We extend earlier work of Cairns (1998), Chaplin (1998) and Feldman et al. (1998), by presenting new theoretical results and also by demonstrating that the same model can be applied to countries other than the United Kingdom. First, we prove that the process of fitting a yield curve to price data has a unique optimal solution in both zero-coupon-bond and low-coupon-bond markets. Furthermore, an alternative method of curve fitting to those proposed previously is shown to have a unique solution in all markets.

The restricted-exponential model has previously been applied to U.K. data (Cairns, 1998). Here, we consider its wider application in European bond markets. In particular, we analyse German market data and conclude that the same model applies equally well to both countries.

We analyse a class of diffusion models that (i) allows an explicit expression for the likelihood function of discrete time observation, (ii) allows the possibility of heavy-tailed observations, and (iii) allows an analysis of the tails of the increments. The class simply consists of transformed Ornstein–Uhlenbeck processes and is of relevance for heavy-tailed time series. We also treat the question of the existence of an equivalent martingale measure for the class of models considered.