We provide a quick glance into recently developed Adaptive Multilevel Monte Carlo (MLMC) Methods for the following widely applied mathematical models: (i) Itô Stochastic Differential Equations, (ii) Stochastic Reaction Networks modeled by Pure Jump Markov Processes, and (iii) Partial Differential Equations with random inputs. In this context, the notion of adaptivity includes several aspects such as mesh refinements based on either a priori or a posteriori error estimates, the local choice of different time-stepping methods, and the selection of the total number of levels and the number of samples at different levels.
For the last two years, Hakon has been a postdoctoral fellow at KAUST with both the Stochastic Numerics research group and the Uncertainty Quantification SRI center. Hakon is an applied mathematician with a strong focus on numerical analysis and algorithmic developments for stochastic differential equations (SDE) and stochastic modeling in general. During his tenure at KAUST, his main efforts have been devoted to the analysis and development of adaptive multilevel Monte Carlo methods for SDEs.