We commonly refer to state estimation theory in geosciences as data assimilation (DA). This
term encompasses the entire sequence of operations that, starting from the observations of a …

The subject of inverse problems in differential equations is of enormous practical
importance, and has also generated substantial mathematical and computational …

This open-access textbook's significant contribution is the unified derivation of data-
assimilation techniques from a common fundamental and optimal starting point, namely …

Fix a domain\mathcal S ⊂ R^ k (our solvency region) and let Y (t)= Y^(u)(t) be a stochastic
process of the form d Y (t) &= b (Y (t), u (t)) d t+ σ (Y (t), u (t)) d B (t)\nonumber\&\quad+ ∫ …

This book aims to take a reader, with a basis in classical real analysis, through the theory of
stochastic processes, the stochastic calculus, applications in control and filtering. The aim is …

In this chapter the state-of-the-art in data assimilation for high-dimensional highly nonlinear
systems is reviewed, and recent developments are highlighted. This knowledge is available …

This book is a substantially revised and expanded edition reflecting major developments in
stochastic numerics since the 1st edition [314] was published in 2004. The new topics …

A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …

In this book the authors describe the principles and methods behind probabilistic forecasting
and Bayesian data assimilation. Instead of focusing on particular application areas, the …

A nonlinear Markov evolution is a dynamical system generated by a measure-valued
ordinary differential equation with the specific feature of preserving positivity. This feature …