Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.
Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.
This book discusses historical continuities and discontinuities between the Polish-Lithuanian Commonwealth, interwar Poland, the Polish People’s Republic, and contemporary Poland. The year 1989 is seen as a clear point-break that allowed the Poles and their country to regain a ‘natural historical continuity’ with the ‘Second Republic,’ as interwar Poland is commonly referred to in the current Polish national master narrative. In this pattern of thinking about the past, Poland-Lithuania (nowadays roughly coterminous with Belarus, Latvia, Lithuania, Poland, Russia’s Kaliningrad Region and Ukraine) is seen as the ‘First Republic.’ However, in spite of this ‘politics of memory’ (Geschichtspolitik) – regarding its borders, institutions, law, language, or ethnic and social makeup – present-day Poland, in reality, is the direct successor to and the continuation of communist Poland. Ironically, today’s Poland is very different, in all the aforementioned aspects, from the First and Second Republics. Hence, contemporary Poland is quite un-Polish, indeed, from the perspective of Polishness defined as a historical (that is, legal, social, cultural, ethnic and political) continuity of Poland-Lithuania and interwar Poland.
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