Expectations

2021 ◽  
pp. 171-189
Author(s):  
James Davidson

The expectation is defined, applying integration concepts to probability measures. Leading examples are given and the different characterizations of the expectation of a function are compared. The Markov and Jensen inequalities are given and consideration of multivariate distributions then leads to the treatment of the Cauchy–Schwarz, Hölder, Liapunov, Minkowski, and Loève inequalities. The final section treats the calculus of random functions of a real variable.

1973 ◽  
Vol 10 (1) ◽  
pp. 109-121 ◽  
Author(s):  
Torgny Lindvall

This paper extends the theory of weak convergence of probability measures and random functions in the function space D[0,1] to the case D [0,∞), elaborating ideas of C. Stone and W. Whitt. 7)[0,∞) is a suitable space for the analysis of many processes appearing in applied probability.


1995 ◽  
Vol 15 (3) ◽  
pp. 413-447 ◽  
Author(s):  
Thomas Bogenschütz ◽  
Volker Mathias Gundlach

AbstractWe consider a Ruelle—Perron—Frobenius type of selection procedure for probability measures that are invariant under random subshifts of finite type. In particular we prove that for a class of random functions this method leads to a unique probability exhibiting properties that justify the names Gibbs measure and equilibrium states. In order to do this we introduce the notion of bundle random dynamical systems and provide a theory for their invariant measures as well as give a precise definition of Gibbs measures.


1973 ◽  
Vol 10 (01) ◽  
pp. 109-121 ◽  
Author(s):  
Torgny Lindvall

This paper extends the theory of weak convergence of probability measures and random functions in the function space D[0,1] to the case D [0,∞), elaborating ideas of C. Stone and W. Whitt. 7)[0,∞) is a suitable space for the analysis of many processes appearing in applied probability.


1980 ◽  
Vol 19 (03) ◽  
pp. 125-132
Author(s):  
G. S. Lodwick ◽  
C. R. Wickizer ◽  
E. Dickhaus

The Missouri Automated Radiology System recently passed its tenth year of clinical operation at the University of Missouri. This article presents the views of a radiologist who has been instrumental in the conceptual development and administrative support of MARS for most of this period, an economist who evaluated MARS from 1972 to 1974 as part of her doctoral dissertation, and a computer scientist who has worked for two years in the development of a Standard MUMPS version of MARS. The first section provides a historical perspective. The second deals with economic considerations of the present MARS system, and suggests those improvements which offer the greatest economic benefits. The final section discusses the new approaches employed in the latest version of MARS, as well as areas for further application in the overall radiology and hospital environment. A complete bibliography on MARS is provided for further reading.


Author(s):  
Peter Hopkins

The chapters in this collection explore the everyday lives, experiences, practices and attitudes of Muslims in Scotland. In order to set the context for these chapters, in this introduction I explore the early settlement of Muslims in Scotland and discuss some of the initial research projects that charted the settlement of Asians and Pakistanis in Scotland’s main cities. I then discuss the current situation for Muslims in Scotland through data from the 2011 Scottish Census. Following a short note about the significance of the Scottish context, in the final section, the main themes and issues that have been explored in research about Muslims in Scotland.


2005 ◽  
Vol 84 (1) ◽  
pp. 1-37 ◽  
Author(s):  
A. A. M. Duncan

The hitherto accepted date of the priory's foundation, 1144, was copied on the bishop's diploma from the bull of Lucius II, and is impossible; Bower's 1140 is to be preferred. The foundation narrative (FN) probably by Robert, the first prior, ascribes to a Pictish king the grant to St Andrew of the Boar's Raik, but that was ignored by Wyntoun and Bower and is probably wrong. It seems that Alexander I made this gift, renegued on it, and restored it towards the end of his life. Though intended to found an Augustinian priory, the Raik was kept by the bishop until in 1138-9 David I obtained from Nostell a prior, Robert; Robert was unable to advance the foundation through his reluctance to recruit canons from elsewhere, perhaps resisting Scone and/or Holyrood. He and clerics of his resided in a ‘parsonage’, the vacant house of one of the seven ‘parsons’ who represented the earliest clerics of St Andrews, and are uniquely described in FN; they developed the hospital. In 1140 David I and Earl Henry at St Andrews compelled the bishop to disgorge the Raik and thereby establish the priory. The date was probably St Andrew's day, 1140, a month after the foundation of the abbey of St Mary at Newbattle. Both foundations should be seen as thanksgiving for Henry's recovery from serious illness. A narrower dating is suggested for some St Andrews charters, the endowments showing a closer relationship with those of Holyrood abbey than with those of Scone priory. Prior Robert probably wished from the beginning to recruit the céli Dé (Culdees) as canons and to obtain their endowments, succeeding at Lochleven but, despite papal and royal approval, failing at St Andrews. A final section asks why David I was so generous to the regular orders, suggesting that he was much influenced by the development of Marian devotion in his lifetime, when the Virgin had become head and most powerful of the hierarchy of saints.


2012 ◽  
Vol 1 (1) ◽  
pp. 83-107 ◽  
Author(s):  
Karen Tracy

This study analyzes public hearings about same-sex marriage to show how the contexts that are established for citizens' and legislators' talk make arguments about the issue being disputed. Situated within the traditions of argument studies and discourse analysis, the article explores different meanings of “context.” The study evidences how two sets of context features created positive (or negative) stances toward the issue of same-sex marriage, and shows that how the controversy was formulated and how participation was designed gave distinct advantages to speakers advocating for (or against) same-sex marriage. The final section draws out implications of these legislative choices for citizen presenters and for the officials themselves as the enactors and guardians of democratic process.


1999 ◽  
Vol 30 (2) ◽  
pp. 653
Author(s):  
Richard Boast
Keyword(s):  

This article introduces the final section of this issue of the Victoria University of Wellington Law Review, which contrasts the work of Professor Richard Maclaurin and Judge Acheson.


2020 ◽  
Author(s):  
William Abbiss

This article offers a ‘post-heritage’ reading of both iterations of Upstairs Downstairs: the LondonWeekend Television (LWT) series (1971–5) and its shortlived BBC revival (2010–12). Identifying elements of subversion and subjectivity allows scholarship on the LWT series to be reassessed, recognising occasions where it challenges rather than supports the social structures of the depicted Edwardian past. The BBC series also incorporates the post-heritage element of self-consciousness, acknowledging the parallel between its narrative and the production’s attempts to recreate the success of its 1970s predecessor. The article’s first section assesses the critical history of the LWT series, identifying areas that are open to further study or revised readings. The second section analyses the serialised war narrative of the fourth series of LWT’s Upstairs, Downstairs (1974), revealing its exploration of female identity across multiple episodes and challenging the notion that the series became more male and upstairs dominated as it progressed. The third section considers the BBC series’ revised concept, identifying the shifts in its main characters’ positions in society that allow the series’ narrative to question the past it evokes. This will be briefly contrasted with the heritage stability of Downton Abbey (ITV, 2010–15). The final section considers the household of 165 Eaton Place’s function as a studio space, which the BBC series self-consciously adopts in order to evoke the aesthetics of prior period dramas. The article concludes by suggesting that the barriers to recreating the past established in the BBC series’ narrative also contributed to its failure to match the success of its earlier iteration.


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