Branching Processes in Random Environment provides a unique and new approach to study branching processes in random environments. Branching processes in random environment are an important direction of the general theory of branching processes which, in turn, is a well-developed part of probability theory having various applications in physics and biology. There are several books devoted to the theory of branching processes; however, the theory of branching processes in random environments is not examined in-depth in those books. During the last two decades essential progress was achieved in this field in particular, due primarily to the authors' efforts. Features a unique and new approach to study branching processes in random environments Compares properties of branching processes in random environments with properties of ordinary random walks Enables finding the probability of survival of the critical and subcritical branching processes in random environments, as well as Yaglom-type limit theorems for the mentioned classes of processes
The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of this theory and presents additional results which establish connections to other areas of mathematics. The arrangement of the material should allow the adoption of this textbook in differently composed Bachelor programmes.
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of this theory and presents additional results which establish connections to other areas of mathematics. The arrangement of the material should allow the adoption of this textbook in differently composed Bachelor programmes.
This volume proposes a theory of history education in formal classroom settings. Specifically, it aims to outline how the particular setting of the classroom interacts with domain-specific processes of historical thinking. The theory rests on the notion that formal school education is a communicative and social system, while historical thinking occurs in the psychological system of a person's historical consciousness. In the complex interaction of these systems, historical thinking, emotions, communication, media and language are of particular importance. Drawing upon educational theory as well as the theory of history, this theory of the history classroom provides a framework as well as a solid foundation for future empirical research, both for developing research questions as well as for interpreting findings.
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