Overview

This text in biomathematics includes new models of stochastic non-linear biological systems and new results for these systems in 2003. These results are based on the new results for non-linear difference and differential equations in random media. The book contains new stochastic non-linear models of biological systems, such as biological systems in random media - epidemic, genetic selection, demography, branching, logistic growth and predator-prey models. It includes results for scalar and vector difference equations in random media with applications to the stochastic biological systems and provides results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability.

Full Product Details

Author:   Anatoly Swishchuk ,  Jianhong Wu
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   18
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.140kg
ISBN:  

9781402015540

ISBN 10:   1402015542
Pages:   218
Publication Date:   31 October 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Preface. List of Notations. 1: Random Media. 1.1. Markov Chains. 1.2. Ergodicity and Reducibility of Markov Chains. 1.3. Markov Renewal Processes. 1.4. Semi-Markov Processes. 1.5. Jump Markov Processes. 1.6. Wiener Processes and Diffusion Processes. 1.7. Martingales. 1.8. Semigroups of Operators and their Generators. 1.9. Martingale Characterization of Markov and Semi-Markov Processes. 1.10. General Representation and Measurability of Biological Systems in Random Media. 2: Limit Theorems for Difference Equations in Random Media. 2.1. Limit Theorems for Random Evolutions. 2.2. Averaging of Difference Equations in Random Media. 2.3. Diffusion Approximation of Difference Equations in Random Media. 2.4. Normal Deviations of Difference Equations in Random Media. 2.5. Merging of Difference Equations in Random Media. 2.6. Stability of Difference Equations in Random Media. 2.7. Limit Theorems for Vector Difference Equations in Random Media. 3: Epidemic Models. 3.1. Deterministic Epidemic Models. 3.2. Stochastic Epidemic Model (Epidemic Model in Random Media). 3.3. Averaging of Epidemic Model in Random Media. 3.4. Merging of Epidemic Models in Random Media. 3.5. Diffusion Approximation of Epidemic Models in Random Media. 3.6. Normal Deviations of Epidemic Model in Random Media. 3.7. Stochastic Stability of Epidemic Model. 4: Genetic Selection Models. 4.1. Deterministic Genetic Selection Models. 4.2. Stochastic Genetic Selection Model (Genetic Selection Model in Random Media). 4.3. Averaging of Slow Genetic Selection Model in Random Media. 4.4. Merging of Slow Genetic Selection Model in Random Media. 4.5. Diffusion Approximation of Slow Genetic Selection Model in Random Media. 4.6. Normal Deviations of Slow Genetic Selection Model in Random Media. 4.7. Stochastic Stability of Slow Genetic Selection Model. 5: Branching Models. 5.1. Branching Models with Deterministic Generating Function. 5.2. Branching Models in Random Media. 5.3. Averaging of Branching Models in Random Media. 5.4. Merging of Branching Model in Random Media. 5.5. Diffusion Approximation of Branching Process in Random Media. 5.6. Normal Deviations of Branching Process in Random Media. 5.7. Stochastic Stability of Branching Model in Averaging and Diffusion Approximation Schemes. 6: Demographic Models. 6.1. Deterministic Demographic Model. 6.2. Stochastic Demographic Models (Demographic Models in Random Media). 6.3. Averaging of Demographic Models in Random Media. 6.4. Merging of Demographic Model. 6.5. Diffusion Approximation of Demographic Model. 6.6. Normal Deviations of Demographic Models in Random Media. 6.7. Stochastic Stability of Demographic Model in Averaging and Diffusion Approximation Schemes. 7: Logistic Growth Models. 7.1. Deterministic Logistic Growth Model. 7.2. Stochastic Logistic Growth Model (Logistic Growth Model in Random Media). 7.3. Averaging of Logistic Growth Model in Random Media. 7.4. Merging of Logistic Growth Model in Random Media. 7.5. Diffusion Approximation of Logistic Growth Model in Random Media. 7.6. Normal De

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