Probability Theory is a branch of science dealing with random events. It provides mathematical tools for evaluating chances, forecasting possible outcomes, and suggesting optimal choices in the presence of uncertainty. The theory of sums of random variables lies at the heart of research in Probability Theory. It is truly fundamental when dealing with the aggregate effect of random events, e.g., when observing the combined effect of a large number of small or rare random contributions. The work on the theory of sums of random variables started in the 17th century, and continued ever since. Among famous contributors are Bernoulli, de Moivre, Laplace, and other well-known mathematicians. Their results have shaped modern Probability Theory. The actual distribution of a sum of random variables is typically complex, and one would prefer using a simpler and more tractable approximate distribution (e.g., normal, Poisson or compound Poisson). However, one can only substitute a complex actual distribution by an approximate one if there is a sharp estimate of the accuracy of approximation indicating the error would be "small". As a result, a lot of work in Probability Theory has been devoted to evaluating the accuracy of approximation. In particular, work on the accuracy of normal approximation to the distributions of sums of random variables started in the late 19th century, and still continues. However, in situations where one deals with rare events a natural approximating distribution is Poisson (or, more generally, compound Poisson). The class of compound Poisson laws is so general that the class of all possible limit laws to the distributions of sums of asymptotically "small" random variables (the class of so-called infinitely divisible distributions) coincides with the class of weak limits of compound Poisson distributions. Poisson and compound Poisson approximations naturally arise when one deals with the number of long head runs is discrete random sequences, the number of long match patterns in DNA sequences, aggregate claims to a (re)insurance company, the number of exceedances of high thresholds in extreme value theory, etc.. The approximation of a complex actual distribution by a Poisson and compound Poisson one is only justified if there is a sharp estimate of the accuracy of approximation indicating the error is "small". Hence the need of sharp estimates of the accuracy of approximation. The proposed research will concentrate on establishing sharp estimates of the accuracy of Poisson and compound Poisson approximation to the distribution of a sum of random variables. In particular, we aim to address a long-standing open question concerning establishing an estimate of the accuracy of (compound) Poisson approximation with a correct (the best possible) constant at the leading term.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

In the form of an artist's book and e-book, Golden (Notes) will document and critically reflect upon the various visual, audio, installation and live strategies of four related works (Golden (Vistas}, Golden (Songs), Golden (Years) and Golden (Voices)), to be exhibited at Beaconsfield and Chinese Arts Centre between 2005 and 2006. The e/book will include an experimental text­ work that will first appear as periodic posts to an online 'blog' or journal for the duration of the e/book's development. In addition, four writers/practitioners will be commissioned to research and develop original texts, which expand both conceptually and formally on the issues, concepts and themes explored in the series. Working across visual and audio culture, literature, choreography, and film, the progressive production of texts will be punctuated by formal and informal dialogues on- and off-line. In sum, the resulting outputs will comprise a limited edition artist's book, an e-book distributed as both limited edition CD-rom and unlimited PDF download, a blog, and gallery-based and online discussions. The research will thereby reach academics, artists, students, contemporary art audiences, internet users, and those with particular interests in theories, practices and interdisciplinary tactics of cultural representation, production and dissemination, in and of diaspora.

Doctoral Training Partnerships: a range of postgraduate training is funded by the Research Councils. For information on current funding routes, see the common terminology at https://www.ukri.org/apply-for-funding/how-we-fund-studentships/. Training grants may be to one organisation or to a consortia of research organisations. This portal will show the lead organisation only.