PHD ORAL PRESENTATION
In recent times, practical problems of interest such as continuous time processes and its applications have attracted a lot of scientific research. Typical computational issues arising from these problems is the computation of expectations of functional of these processes. This has called for developing fast computational methods to achieve accurate estimates at a minimal cost in solving these problems. Efficient algorithms are then needed to handle the computational burden associated with solving these continuum problems. This thesis addresses these issues by developing and applying one of these algorithms, called the multilevel particle filter (MLPF), for inference problems arising in solving these continuum problems such as stochastic differential equation. The continuous time processes considered are diffusion processes and general Levy processes. The computational savings obtained in applying the multilevel particle filter compared with the standard particle filter (PF) is illustrated with several practical application problems. We address several inference problems arising from these processes such as estimation of marginal likelihoods, pricing of financial derivatives and filtering of partially observed Levy processes and demonstrate reduced computational cost attained when our proposed novel MLPF method is applied.