Fast Variables in Stochastic Population Dynamics, Constable George William Albert

Автор: Oksendal
Название: Stochastic Differential Equations
ISBN: 3540047581 ISBN-13(EAN): 9783540047582
Издательство: Springer
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Описание: Gives an introduction to the basic theory of stochastic calculus and its applications. This book offers examples in order to motivate and illustrate the theory and show its importance for many applications in for example economics, biology and physics.

Автор: Karatzas
Название: Brownian Motion and Stochastic Calculus
ISBN: 0387976558 ISBN-13(EAN): 9780387976556
Издательство: Springer
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Описание: This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.

Автор: George William Albert Constable
Название: Fast Variables in Stochastic Population Dynamics
ISBN: 3319212176 ISBN-13(EAN): 9783319212173
Издательство: Springer
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Цена: 102480.00 T
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Описание: In this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike. Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem. When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply. While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology.