Selected Topics In Mathematical Modelling: Machine Learning And Tugs-of-war

This thesis consists of four scientific articles that explore topics in mathematical modelling, specifically machine learning and stochastic games called tugs-of-war. Article I presents an ensemble of independent and parallel long short-term memory (LSTM) neural networks for the prediction of financial time series. Article II delves into the high-dimensional parameter space in which the optimization of deep neural networks occurs. Article III proves asymptotic mean value representation formulas for functions with respect to the fractional heat operator. Article IV introduces a new class of strongly degenerate nonlinear parabolic partial differential equations (PDEs).