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| Modelling Explosive Random Processes |
| | Many stochastic models account for explosive behaviour by allowing infinitely many transitions in a finite time. As a result, there can be a range of processes sharing the same parameters. It is therefore important to be able to identify those processes that satisfy some additional criteria. I have adopted a fresh approach based on approximating the transition probabilities of the process. We hope that these methods will provide a computationally effective means for describing the long-term behaviour of these processes. |
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| Operator-Analytic Methods in Telecommunication Systems |
| | Developing techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many complex systems, such as the Internet. We will develop efficient numerical algorithms that will make possible practical analysis of operator-analytic models. |
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| Modelling Evanescent Random Processes |
| | The aim is to develop analytical and computational techniques for evaluating quasi-stationary distributions. These are mathematical tools that allow one to model the long-term behaviour of evanescent random processes that arise in biology, chemistry and telecommunications. |
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| Assessing the Performance of Telecommunications Networks |
| | The broad aim is to improve procedures for evaluating the performance of telecommunications networks by proposing several new models that account for dependencies between neighbouring communications links. |
