This book offers an overview of diffusion processes as an instrument for realistically modelling the time-continuous evolution of phenomena in the natural sciences as well as in finance and economics. The theory is demonstrated using real data applications.

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.

Explicit instructions for diffusion modelling enable practitioners to apply this powerful class of processes Both stochastic modelling and statistical inference for diffusion processes are comprehensively covered in one book Explains in detail a Bayesian approach which enables parameter estimation for diffusion models in many applications in life sciences Graphical illustrations facilitate the understanding of Bayesian imputation techniques and associated convergence considerations Methods are illustrated on complex real data applications from epidemic modelling and fluorescence microscopy Required knowledge on stochastic calculus is provided in a special chapter Includes supplementary material: sn.pub/extras

Autorentext

Christiane Fuchs received an MSc degree in Computational Mathematics from Brunel University West London in 2003 and a Diploma in Mathematics from the University of Hanover in 2005. In 2010 she completed her doctorate in Statistics at the Ludwig-Maximilians-Universität Munich.

After an interim research stay at the University of Warwick in 2010 she is currently a postdoctoral fellow at the Helmholtz Centre in Munich.

Inhalt
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.