New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for perf ....New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for performing statistical inference on the long memory models. The accuracy of numerical approximations will be analysed using simulations on supercomputers. Expected outcomes include models and results of practical importance with applications such as intrusion detection problems, cell motility for biological data and telecommunication.Read moreRead less
Propagation via nonlinear partial differential equations. This project aims to develop new theories in nonlinear partial differential equations to better understand propagation phenomena. Propagation occurs in various forms, such as the spreading of invasive species, infectious diseases or cancer cells, or the progression of the healing front of a wound. This project aims to understand propagation speed and profile, criteria for spreading and vanishing, and other qualitative properties of the eq ....Propagation via nonlinear partial differential equations. This project aims to develop new theories in nonlinear partial differential equations to better understand propagation phenomena. Propagation occurs in various forms, such as the spreading of invasive species, infectious diseases or cancer cells, or the progression of the healing front of a wound. This project aims to understand propagation speed and profile, criteria for spreading and vanishing, and other qualitative properties of the equations. The project will develop new mathematical theories, and build bridges between the theories and applications.Read moreRead less