Stochastic processes of common use in mathematical finance are presented in this book, which interlaces financial concepts and instruments such as arbitrage opportunities, option pricing and default ...risk with Brownian motion and Lévy and diffusion processes.
Focuses on applications of demographic models. This book introduces the life table to describe age-specific mortality, and uses it to develop theory for stable populations and the rate of population ...increase. This theory is then revisited in the context of matrix models, for stage-classified as well as age-classified populations.
These notes are based on a course of lectures given by Professor
Nelson at Princeton during the spring term of 1966. The subject of
Brownian motion has long been of interest in mathematical
...probability. In these lectures, Professor Nelson traces the history
of earlier work in Brownian motion, both the mathematical theory,
and the natural phenomenon with its physical interpretations. He
continues through recent dynamical theories of Brownian motion, and
concludes with a discussion of the relevance of these theories to
quantum field theory and quantum statistical mechanics.
From clocks to chaos Glass, Leon; Mackey, Michael C
1988, 2020, 2020-11-10
eBook, Book
In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed ...include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics. Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.
Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a ...wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.
Spatial Ecology addresses the fundamental effects of space on the dynamics of individual species and on the structure, dynamics, diversity, and stability of multispecies communities. Although the ...ecological world is unavoidably spatial, there have been few attempts to determine how explicit considerations of space may alter the predictions of ecological models, or what insights it may give into the causes of broad-scale ecological patterns. As this book demonstrates, the spatial structure of a habitat can fundamentally alter both the qualitative and quantitative dynamics and outcomes of ecological processes. Spatial Ecology highlights the importance of space to five topical areas: stability, patterns of diversity, invasions, coexistence, and pattern generation. It illustrates both the diversity of approaches used to study spatial ecology and the underlying similarities of these approaches. Over twenty contributors address issues ranging from the persistence of endangered species, to the maintenance of biodiversity, to the dynamics of hosts and their parasitoids, to disease dynamics, multispecies competition, population genetics, and fundamental processes relevant to all these cases. There have been many recent advances in our understanding of the influence of spatially explicit processes on individual species and on multispecies communities. This book synthesizes these advances, shows the limitations of traditional, non-spatial approaches, and offers a variety of new approaches to spatial ecology that should stimulate ecological research.
This text offers a unified treatment of blind equalization and system identification that covers theory, performance analysis, simulation, implementation and applications.
How to apply operational risk theory to real-life banking data Modelling Operational and Reputational Risks shows practitioners the best models to use in a given situation, according to the type of ...risk an organization is facing. Based on extensive applied research on operational risk models using real bank datasets, it offers a wide range of various testing models and fitting techniques for financial practitioners. With this book, professionals will have a foundation for measuring and predicting these important intangibles. Aldo Soprano (Madrid, Spain) is Group Head of operational risk management at UniCredit Group.
