Bücher von Gerhard Winkler

An der Staffelei zu stehen, diese Landschaft, diese fast unberührte Natur mit Pinsel und Farbe zu spüren, sie einzuatmen, zu hören oder zu riechen, lässt mich die Zeit vergessen, ist Stille und Ruhe. Welch Reichtum beschert mir der Augenblick, welche innere Zufriedenheit und Ruhe, die mich über das eigene Sein und die Gemeinschaft nachdenken lässt. Bewusst wird mir, welcher Naturbesitz uns hier anvertraut ist wie auch die Frage, wie wir wohl mit diesem Schatz in der nahen Zukunft umgehen werden. Nicht das Abbild des Gesehenen ist für mich beim Malen wichtig, vielmehr ist es das durchdringende Sehen und die damit verbundenen Gedanken und Ahnungen, die sichtbar werden - das Spüren, dass ich selbst Teil dieses unergründlichen Schatzes bin. Bescheiden stehe ich so an meiner Staffelei.

This text introduces at a moderate speed and in a thorough way the basic concepts of the theory of stochastic integrals and Ito calculus for sem i­ martingales. There are many reasons to study this subject. We are fascinated by the contrast between general measure theoretic arguments and concrete probabilistic problems, and by the own flavour of a new differential calculus. For the beginner, a lot of work is necessary to go through this text in detail. As areward it should enable her or hirn to study more advanced literature and to become at ease with a couple of seemingly frightening concepts. Already in this introduction, many enjoyable and useful facets of stochastic analysis show up. We start out having a glance at several elementary predecessors of the stochastic integral and sketching some ideas behind the abstract theory of semimartingale integration. Having introduced martingales and local martingales in chapters 2 - 4, the stochastic integral is defined for locally uniform limits of elementary processes in chapter S. This corresponds to the Riemann integral in one-dimensional analysis and it suffices for the study of Brownian motion and diffusion processes in the later chapters 9 and 12.

"This book is concerned with a probabilistic approach for image analysis, mostly from the Bayesian point of view, and the important Markov chain Monte Carlo methods commonly used....This book will be useful, especially to researchers with a strong background in probability and an interest in image analysis.

This text is concerned with a probabilistic approach to image analysis as initiated by U. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging.