Central and non-central limit theorems for weighted power variations of fractional Brownian motion

In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q>=2 of the fractional Brownian motion with Hurst parameter H in (0,1), where q is an integer. The central limit holds for 1/(2q)<H<= 1-1/(2q), the limit being a conditionally Gaussian distribution. If H<1/(2q), we show the convergence in L^2 to a limit which only depends on the fractional Brownian motion, and if H> 1-1/(2q), we show the convergence in L^2 to a stochastic integral with respect to the Hermite process of order q.Comment: 30 pages; minor change

A Causal Comparative Study Of Student Success And Retention In An Undergraduate Program Offered Online And On Campus

Online education has grown significantly both in the number of courses offered and the number of degrees offered. The delivery format is being fueled by a student population that is growing more non-traditional. Work and family obligations dictate that classes are offered in a format that meets the needs of the students. The growth of universities toward online courses and degrees has brought opportunities to students, but it has also given institutions of higher education new income streams. In the case of public universities in Kentucky, this has helped offset reductions in state support. The viability of this format for course delivery rests in the success of those enrolled in those courses and programs. This study seeks to determine if students entering an online, undergraduate degree program at a state comprehensive university in the southeastern United States, perform at the same level, as measured by the grade earned in an introductory level major-program course, and persist at similar rates, as measured by first to second year retention. The effect of covariates on the online and on-campus outcomes were examined

Structural approaches to protein sequence analysis

Various protein sequence analysis techniques are described, aimed at improving the prediction of protein structure by means of pattern matching. To investigate the possibility that improvements in amino acid comparison matrices could result in improvements in the sensitivity and accuracy of protein sequence alignments, a method for rapidly calculating amino acid mutation data matrices from large sequence data sets is presented. The method is then applied to the membrane-spanning segments of integral membrane proteins in order to investigate the nature of amino acid mutability in a lipid environment. Whilst purely sequence analytic techniques work well for cases where some residual sequence similarity remains between a newly characterized protein and a protein of known 3-D structure, in the harder cases, there is little or no sequence similarity with which to recognize proteins with similar folding patterns. In the light of these limitations, a new approach to protein fold recognition is described, which uses a statistically derived pairwise potential to evaluate the compatibility between a test sequence and a library of structural templates, derived from solved crystal structures. The method, which is called optimal sequence threading, proves to be highly successful, and is able to detect the common TIM barrel fold between a number of enzyme sequences, which has not been achieved by any previous sequence analysis technique. Finally, a new method for the prediction of the secondary structure and topology of membrane proteins is described. The method employs a set of statistical tables compiled from well-characterized membrane protein data, and a novel dynamic programming algorithm to recognize membrane topology models by expectation maximization. The statistical tables show definite biases towards certain amino acid species on the inside, middle and outside of a cellular membrane

A consideration of the current view and history of the people of Canvey Island, Essex, in the context of modern England with regard to the place of the church in community particularly in the face of bereavement and the conduct of funeral rites.

This study is the result of six years of part-time research by a practising Church of England minister. It focusses on the people of Canvey Island in Essex from the early 20th century when the church held sway over every aspect of their lives, to the present day when engagement with the church is one option of many. The study seeks to show how and why many who belong to no church congregation still call on the church at a time of bereavement and how the church might better recognise and sanctify the language and practice of those who would not call themselves religious. The thesis explores the many-faceted and often contradictory contextual issues of contemporary ministry with particular focus on the whole gamut of funeral ministry from miscarriage and neo-natal death to a death occurring naturally in old age. It examines the relationship between the intrinsic and the vernacular on the one hand and the language of the established church on the other. It recognises the so-called folk religion as the basic longing of humanity for meaning and order in a chaotic and seemingly random life: a longing which the church has largely adopted, organised, formalised, institutionalised and often fossilized. It considers how such desire is met by Civil celebrants and others if church ministers are slow to respond to the need. In this third decade of the twenty-first century, society is at a crucial crossroad with regard to the way in which we handle death, grief and an understanding of on-going life which survives the physical. A society increasingly at home with the connectedness of everything through the internet requires a church that understands and recognises its language and its longing. This thesis repeatedly addresses the ways that the church and its ministers need to embrace its changing role, particularly at the time of death. The author’s upbringing in the British West Indies is very different from that of the people of Canvey Island. In distilling the fruit of twenty-four years of ministry among them, he has sought to use readily intelligible language to tell the stories of the dying and the bereaved and to bring to bear academic studies from the fields of sociology, anthropology and theology in the context and light of the lived experience of parish life

The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals

The aim of this paper is to show an estimate for the determinant of the covariance of a two-dimensional vector of multiple stochastic integrals of the same order in terms of a linear combination of the expectation of the determinant of its iterated Malliavin matrices. As an application, we show that the vector is not absolutely continuous if and only if its components are proportional