Summing up the authors research in the mathematics of error, this book is geared towards both theory and applications. On the one hand, it aims to set error calculus on rigorous mathematical foundations, on the other, it applies the theoretical machinery to complex models where random processes intervene. Even though it starts as an easy-to-follow introduction for the beginning graduate student, it leads the reader to recent research developments in stochastic analysis and Malliavin calculus. To do so, error theory is presented in a progressive way, based on the practitionners intuition about error calculations. This should help the reader develop hands-on operational skills for error calculations on finite dimensional complex models. The intuitive idea of error is then axiomatized by the notion of in order to be applied in more general mathematical frameworks such as those found in signal processing or finance. The theory of error structures is a powerful analytical tool that allows one to view Malliavin's calculus as a transversal error calculus on the trajectories of Brownian motion. Throughout the book, numerous applications in different areas such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are worked out in detail through concrete examples. weiterlesen