Stefan Geiss – författare

We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space.The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivatives in the Malliavin sense without computing or accessing these Malliavin derivatives explicitly.Regarding BSDEs, we deduce regularity properties of the solution processes from the Besov regularityof the initial data, in particular upper bounds for their Lp-variation, where the generator might be of quadratic type and where no structural assumptions, for example in terms of aforward diffusion, are assumed. As an example we treat sub-quadratic BSDEs with unbounded terminal conditions.Among other tools, we use methods from harmonic analysis. As a by-product, we improve the asymptotic behaviour of the multiplicative constant in a generalized Fefferman inequality and verify the optimality of the bound we established.

This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional analysis.The initial chapters provide a rigorous introduction to measure theory, with a special focus on probability spaces. Next, Lebesgue integration theory is developed in full detail covering the main methods and statements, followed by the important limit theorems of probability. Advanced limit theorems, such as the Berry-Esseen Theorem and Stein’s method, are included. The final part of the book explores interactions between probability and functional analysis. It includes an introduction to Banach function spaces, such as Lorentz and Orlicz spaces, and to random variables with values in Banach spaces. The Itô–Nisio Theorem, the Strong Law of Large Numbers in Banach spaces, and the Bochner, Pettis, and Dunford integrals are presented. As an application, Brownian motion is rigorously constructed and investigated using Banach function space methods.Based on courses taught by the authors, this book can serve as the main text for a graduate-level course on probability, and each chapter contains a collection of exercises. The unique combination of probability and functional analysis, as well as the advanced and original topics included, will also appeal to researchers working in probability and related fields.

​Die 2008 einsetzende Rezession – meist als „Weltfinanz-“ oder „Weltwirtschaftskrise“ bezeichnet – provozierte in Bevölkerung, Wirtschaft und Politik Forderungen nach staatlichen Eingriffen zur Milderung der Krisenfolgen. Zu den prominentesten Beispielen gehören die Diskussionen um die Verstaatlichung der HRE und um Finanzhilfen für den Automobilhersteller Opel. Das Buch beleuchtet, wie maßgebliche Nachrichtenmedien die Forderung nach staatlicher Intervention aufgriffen und bewerteten. Im Mittelpunkt steht, welche Arten staatlicher Eingriffe auf Unterstützung und welche auf Ablehnung stießen, welche Akteure ihre Standpunkte in den medialen Diskurs einbringen konnten, und mit welchen kommunikativen Strategien diese Standpunkte gerechtfertigt wurden.​