Stochastic Differential Equations

Many processes in the life sciences are stochastic in nature and Stochastic Differential Equations (SDEs) and Data Assimilation (DA) are fields that combine data and statistics with mathematical modelling to effectively model these stochastic processes, something that not always can be achieved with deterministic models. Examples range from modelling viral infections and water pollution in rivers to optimal foraging strategies of animals and climate fluctuations like Dansgaard-Oescher events. Other examples are neural fields used to model brain activity, crop growth modelling and plant breeding. In the past decades, our mathematical and numerical understandings of SDEs and DA have developed significantly, and these new insights are now rapidly being applied in the life sciences. A gentle theoretical introduction to SDEs and DA will be provided, followed by a hands-on, example-driven, approach with the focus on implementation of real-world examples.

After successful completion of this course students are expected to be able to:

• explain and interpret concepts, methods, and techniques from stochastic differential equations and data assimilation;
• recognize questions and situations that profit from an approach using stochastic differential equations or data assimilation;
• apply modern computational approaches for stochastic differential equations and data assimilation;
• effectively set up, perform, and communicate about stochastic differential equations and data assimilation.

Assumed Knowledge:
Mathematics 2 (MAT-14903), Mathematics 3 (MAT-15003) and Statistics 2 (MAT-15403) or equivalent