Stochastic models for increments of EEG recordings using heavy-tailed and fractional diffusions

The goal of this project is to build new stochastic models for the EEG data using stochastic processes, namely heavy-tailed diffusion. Electroencephalogram (EEG) is a record of electrical activity generated by a large number of cortical neurons in the brain. The supervisors have real-world EEG data from African children affected by cerebral malaria, as well as data on subsequent neurodevelopmental and cognitive outcomes of these children. The over-arching goal of the project is to build new stochastic models for the EEG data using stochastic processes, namely heavy-tailed diffusion and fractional diffusion. The proposed new mathematical methods will result in estimation of the EEG parameters, which could predict which children would have neurocognitive deficits after surviving cerebral malaria.
Preliminary analyses of the available EEG data indicate that the increments of EEG recordings for some channels have a normal distribution or Student distribution. Student distribution is a heavy-tailed distribution, so it is preferred for modeling the distribution of recordings in which extreme jumps in brain activity are much more common. Much more interesting histograms are symmetric with two or even three peaks, indicating that the distribution of increments of EEG recordings should be modeled with a new symmetric multimodal distribution