Stochastic models for fractal processes

This paper considers the situation where a stochastic process may display both long-range dependence (LRD) and intermittency. The existence of such a process is established in Anh et al. (1999). Existing works have commonly paid attention either to LRD or intermittency quite separately. This paper offers a convenient framework to study both effects simultaneously. A method is given to estimate and separate the two effects. The wavelet theory plays an essential role in this procedure. Numerical experiments on fractional Brownian motion and multiplicative cascade processes confirm the power of the method.     

Minimum contrast estimation of random processes based on information of second and third orders

This paper presents the results on consistency and asymptotic normality of a class of minimum contrast estimators for random processes with short- or long-range dependence based on the second- and third-order cumulant spectra. Asymptotic properties of sample spectral functionals of second and third orders, which are of independent interest in view of their possible use for nonparametric estimation of processes with short- or long-range dependence, are also provided.     

WHAT IT TAKES TO BE A GRANDPARENT IN A NEW COUNTRY: THE LIVED EXPERIENCE AND EMOTIONAL WELL‐BEING OF AUSTRALIAN‐VIETNAMESE GRANDPARENTS

This study attempts to understand the lived experience and emotional well‐being of Australian‐Vietnamese grandparenthood. Thirty‐six grandparents participated in four focus group interviews while three grandparents took part in individual in‐depth interviews where the experiences of the grandparents were further clarified. The findings reveal that Vietnamese grandparents encounter many changes in their lives and their relationships with their children and grandchildren in their new homeland. However, many still seem to play important roles in the family, creating a vital bridge to grandchildren. According to our participants, the grandparents' most important roles are the maintenance of good emotional relationships and support, and the construction of harmony and continuity in their modified extended families. To be able to assume these roles, grandparents need to actively explore and consider accepting new values. For many, a successful grandparenthood brings happiness to the family, positively influences grandparents' life satisfaction and emotional well‐being, and this in turn enhances their quality of life.     

On LSE in regression model for long-range dependent random fields on spheres

We study the asymptotic behaviour of least squares estimators (LSE) in regression models for long-range dependent random fields observed on spheres. The LSE can be given as a weighted functional of long-range dependent random fields. It is known that in this scenario the limits can be non-Gaussian. We derive the limit distribution and the corresponding rate of convergence for the estimators. The results were obtained under rather general assumptions on the random fields. Simulation studies were conducted to support theoretical findings.     

Continuous-Time Stochastic Processes with Cyclical Long-Range Dependence

This paper introduces continuous‐time random processes whose spectral density is unbounded at some non‐zero frequencies. The discretized versions of these processes have asymptotic properties similar to those of discrete‐time Gegenbauer processes. The paper presents some properties of the covariance function and spectral density as well as a theory of statistical estimation of the mean and covariance function of such processes. Some directions for further generalizations of the results are indicated.     

Lone mothers' time allocations: choices and satisfactions

This paper uses the 2006 Australian Time Use Survey to examine the allocation of time to personal care, employment‐related activities, home duties, leisure and child care of lone mothers, in comparison to the time allocations of single women, women in childless couples and partnered mothers. Both primary and secondary time allocations are considered. The satisfactions that women report concerning their current time allocations are also analysed. The time use and satisfaction data are described using both tabulations and multiple regression methods. Lone mothers are shown to have similar time allocations as the other types of households, even though they have different financial and time resources. This raises the concern that lone mothers' desire or need to maintain such time allocations may lead to task overload. Consistent with this, lone mothers are found to be less satisfied with the way they allocate their time than single women and partnered mothers. The tensions associated with time use among lone mothers discussed in the literature are real, and important.     

A linear programming duality approach to analyzing strictly nonblocking <Emphasis Type="Italic">d</Emphasis>-ary multilog networks under general crosstalk constraints

When a switching network topology is used for constructing optical cross-connects, as in the circuit switching case, no two routes are allowed to share a link. However, if two routes share too many switching elements, then crosstalk introduced at those switching elements degrades signal quality. Vaez and Lea (IEEE Trans. Commun. 48:(2)316–323, 2000) introduced a parameter c which is the maximum number of distinct switching elements a route can share with other routes in the network. This is called the general crosstalk constraint. This paper presents a new method of analyzing strictly nonblocking multi-log networks under this general crosstalk constraint using linear programming duality.