Introduction -- Stochastic Modelling in Life Sciences -- Stochastic Differential Equations and Diffusions in a Nutshell -- Approximation of Markov Jump Processes by Diffusions -- Diffusion Models in Life Sciences -- Parametric Inference for Discretely-observed Diffusions -- Bayesian Inference for Diffusions with Low-frequency Observations -- Application I: Spread of Influenza -- Application II: Analysis of Molecular Binding -- Conclusion and Outlook -- Benchmark Models -- Miscellaneous -- Supplementary Material for Application I -- Supplementary Material for Application II -- Notation -- References.

Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.