This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Rene Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis. Rene Schilling's notes are an expanded version of his course on Levy and Levy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Levy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Levy-Ito decomposition. On the other, it identifies the infinitesimal generator of the Levy process as a pseudo-differential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Levy processes. The presentation is self-contained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. In turn, Davar Khoshnevisan's course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparison-type results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative space-time white noise on a group, and the underlying elliptic operator corresponds to a generator of a Levy process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples.

This volume presents recent developments in the area of Levy-type processes and more general stochastic processes that behave locally like a Levy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Levy-type process: a non-random function which is a counterpart of the characteristic exponent of a Levy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes.

This is the third volume in a subseries of the Lecture Notes in Mathematics called Levy Matters. Each volume describes a number of important topics in the theory or applications of Levy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world."

Studienarbeit aus dem Jahr 2012 im Fachbereich BWL - Allgemeines, Note: 2,3, Universitat Stuttgart (Betriebswirtschaftliches Institut - Abteilung VII - Lehrstuhl fur Allgemeine Betriebswirtschaftslehre und Wirtschaftsinformatik I), Veranstaltung: Informationsmanagement, Sprache: Deutsch, Abstract: Die vorliegende Arbeit beschaftigt sich mit der IT-Unterstutzung in Geschaftsprozessen, insbesondere mit dem Einsatz von ERP- bzw. Enterprise-Resource-Planning-Systemen in Industriebetrieben. Dabei erfolgt zunachst die Darlegung der Grundlagen von ERP-Systemen. Eingegangen wird hierbei auf die Begriffsdefinition, die Herkunft von ERP-Systemen sowie die Abgrenzung zu ERPII-Losungen. Im weiteren Fortgang stehen die Geschaftsprozesse bzw. die Funktionsbereiche, die durch ERP-Systeme in Industriebetrieben Unterstutzung erhalten, im Mittelpunkt. Dabei erfolgt die Betrachtung von ERP-Systemen entlang der Wertschopfungskette. Berucksichtigung findet dabei auch der Prozess der ERP-Auswahl. Abschliessend werden die zukunftigen Chancen und Herausforderungen von ERP-Systemen betrachtet, wobei auf das Zusammenspiel von ERP-Systemen und innovativen IT-Technologien, wie z.B. Cloud Computing, Mobile Computing sowie Social Media, eingegangen wird

Studienarbeit aus dem Jahr 2011 im Fachbereich BWL - Investition und Finanzierung, Note: 1,7, Universitat Stuttgart (Institut fur Volkswirtschaftslehre und Recht ), Veranstaltung: Technisch orientierte Betriebswirtschaftslehre, Sprache: Deutsch, Abstract: Einfuhrend erfolgt die Darlegung der Grundlagen des Ratings unter Berucksichtigung der Herkunft des Ratingbegriffs, der Ratingarten, des Ratingprozesses sowie der Symbolik des Ratings. Anschliessend findet eine Einordung der Ratingagenturen im Zusammenhang mit der globalen Finanzmarktkrise statt, wobei hier auf die Ursachen eingegangen wird. Behandelt wird das Problem der Informationsasymmetrie, welches sich mit dem Principal-Agent-Ansatz darstellen lasst. Zum Schluss erfolgt eine Grobdarstellung der Losungs- bzw. Regulierungsansatze. Eingegangen wird hierbei vorwiegend auf staatliche Regulierungsbemuhungen

This is a concise and elementary introduction to measure and integration theory as it is nowadays needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, differentiation of measures, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions can be found on the authors website, which can be reached from www.cambridge.org/9780521615259.