Multivariate sequential point estimation

For a multivariate normal distribution with unknown mean vector and unknown dispersion matrix, a sequential procedure for estimating the unknown mean vector is suggested. The procedure is shown to be asymptotically “risk efficient” in the sense of Starr (Ann. Math. Statist. (1966), 1173–1185), and the asymptotic order of the “regret” (see Starr and Woodroofe, Proc. Nat. Acad. Sci. 63 (1969), 285–288) is given. Moderate sample behaviour of the procedure using Monte-Carlo techniques is also studied. Finally, the asymptotic normality of the stopping time is proved.     

On the Wang–Uhlenbeck Problem in Discrete Velocity Space

The arguably simplest model for dynamics in phase space is the one where the velocity can jump between only two discrete values, ±v with rate constant k. For this model, which is the continuous-space version of a persistent random walk, analytic expressions are found for the first passage time distributions to the origin. Since the evolution equation of this model can be regarded as the two-state finite-difference approximation in velocity space of the Kramers–Klein equation, this work constitutes a solution of the simplest version of the Wang–Uhlenbeck problem. Formal solution (in Laplace space) of generalizations where the velocity can assume an arbitrary number of discrete states that mimic the Maxwell distribution is also provided.     

Diethoxymethane as tailor-made fuel for gasoline controlled autoignition

Within the cluster of excellence “Tailor-Made Fuels from Biomass”  diethoxymethane (DEM) was identified as a promising fuel candidate from a production perspective. Synthesized by combining a bio-based feedstock and $C{O}_2$ as carbon source together with “green hydrogen” from water electrolysis DEM is defined as “bio-hybrid fuel” . To determine the molecules general applicability to a combustion system and to develop up combustion models a rapid screening of the ignition characteristics is performed in a rapid compression machine and a shock tube. Those suggest DEM being a potential fuel for gasoline controlled autoignition (GCAI) because of a relatively wide range of temperature independent ignition delay, a good autoignition behavior compared to conventional gasoline fuel and a multi-stage ignition behavior. To test the suitability of those molecules as a fuel and determine possible improvements to the production side, DEM was used in a single cylinder research engine operated in GCAI combustion mode. Compared to GCAI combustion with conventional RON95 E10 fuel, DME shows a significantly decreased ignition delay. As a consequence, the internal residual gas fraction, whose enthalpy is used to initiate autoignition, can be reduced and combustion stability is increased. Starting from similar combustion phasing using external exhaust gas recirculation to align the ignition behavior of DEM and RON95 E10, a variation of the intake temperature reveals that DEM has the potential to reduce the sensitivity of the combustion system.     

Uniform-Penalty Inversion of Multiexponential Decay Data: II. Data Spacing, T2 Data, Systematic Data Errors, and Diagnostics

The basic method of UPEN (uniform penalty inversion of multiexponential decay data) is given in an earlier publication (Borgia et al., J. Magn. Reson. 132, 65–77 (1998)), which also discusses the effects of noise, constraints, and smoothing on the resolution or apparent resolution of features of a computed distribution of relaxation times. UPEN applies negative feedback to a regularization penalty, allowing stronger smoothing for a broad feature than for a sharp line. This avoids unnecessarily broadening the sharp line and/or breaking the wide peak or tail into several peaks that the relaxation data do not demand to be separate. The experimental and artificial data presented earlier were T₁ data, and all had fixed data spacings, uniform in log-time. However, for T₂ data, usually spaced uniformly in linear time, or for data spaced in any manner, we have found that the data spacing does not enter explicitly into the computation. The present work shows the extension of UPEN to T₂ data, including the averaging of data in windows and the use of the corresponding weighting factors in the computation. Measures are implemented to control portions of computed distributions extending beyond the data range. The input smoothing parameters in UPEN are normally fixed, rather than data dependent. A major problem arises, especially at high signal-to-noise ratios, when UPEN is applied to data sets with systematic errors due to instrumental nonidealities or adjustment problems. For instance, a relaxation curve for a wide line can be narrowed by an artificial downward bending of the relaxation curve. Diagnostic parameters are generated to help identify data problems, and the diagnostics are applied in several examples, with particular attention to the meaningful resolution of two closely spaced peaks in a distribution of relaxation times. Where feasible, processing with UPEN in nearly real time should help identify data problems while further instrument adjustments can still be made. The need for the nonnegative constraint is greatly reduced in UPEN, and preliminary processing without this constraint helps identify data sets for which application of the nonnegative constraint is too expensive in terms of error of fit for the data set to represent sums of decaying positive exponentials plus random noise.     

Some Martingales Related to the Integral of Brownian Motion. Applications to the Passage Times and Transience

Let (B _t) _t0 be the standard linear Brownian motion started at y and set (X _t, B _t). In this paper we introduce some martingales related to the Markov process (U _t) _t0, which allow us to calculate explicitly the probability laws of several passage times associated to U in a probabilistic way. With the aid of an appropriate supermartingale, we also establish the transience of the process (U _t) _t0.     

双连续N次积分C-半群的逼近定理

在C0半群和双连续半群逼近定理的启发下,讨论了双连续n次积分C-半群的逼近定理.     

Geo/G/1 queues with disasters and general repair times

This paper discusses discrete-time single server Geo/G/1 queues that are subject to failure due to a disaster arrival. Upon a disaster arrival, all present customers leave the system. At a failure epoch, the server is turned off and the repair period immediately begins. The repair times are commonly distributed random variables. We derive the probability generating functions of the queue length distribution and the FCFS sojourn time distribution. Finally, some numerical examples are given.     

指数有界的双连续n次积分C-半群及其生成定理

在双连续半群和n次积分C-半群的基础上,引入了指数有界的双连续n次积分C-半群,并讨论了其性质和生成定理.     

Fisher information in<Emphasis Type="Italic">k</Emphasis>-records

We derive some general results on the Fisher information (FI) contained in the upper (or lower)k-record values and associatedk-record times generated from an i.i.d. sample of fixed size from a continuous distribution. We apply the results to obtain the FI in both upper and lowerk-record data from an exponential distribution. We propose two estimators of the exponential mean, based on the upper and lowerk-record data, and discuss their small sample properties. We also considerk-record data from an inverse sampling plan, and present general formulas for the FI contained in it. Supported in part by Fonde Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) grant # 1020479 of Chile.     

随机波动模型的首中时问题

研究了一类波动率是平方根过程的随机波动CEV模型的首中时问题.利用鞅方法求解首中时和波动率的联合拉普拉斯变换,继而将问题转换为求解一类变系数二阶常微分方程,通过变量代换将此方程转化为经典的Whittaker方程,得到联合拉普拉斯变换表达式.最后,选取不同的参数,使随机波动CEV模型的资产价格过程能够涵盖O-U过程、几何布朗运动、平方根过程等几种常见的扩散过程,画出不同参数下联合拉普拉斯变换函数的三维图像,并分析其变化趋势.