Evolution of Biological Systems in Random Media: Limit Theorems and Stability / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
$132.05
Used and New from Other Sellers
Used and New from Other Sellers
from $24.00
Usually ships in 1-2 business days
(Save 82%)
Other sellers (Hardcover)
  • All (8) from $24.00   
  • New (5) from $24.00   
  • Used (3) from $69.80   

Overview

This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results for non-linear difference and differential equations in random media. This 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;
-New results for scalar and vector difference equations in random media with applications to the stochastic biological systems in 1);
-New results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability;
-New approach to the study of stochastic biological systems in random media such as random evolution approach.

Read More Show Less

Product Details

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. Shastic 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. Shastic Stability of Epidemic Model.
4: Genetic Selection Models. 4.1. Deterministic Genetic Selection Models. 4.2. Shastic Genetic Selection Model (Genetic Selection Model in Random Media). 4.3.4.4. 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. Shastic 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. Shastic Stability of Branching Model in Averaging and Diffusion Approximation Schemes.
6: Demographic Models. 6.1. Deterministic Demographic Model. 6.2. Shastic 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. Shastic Stability of Demographic Model in Averaging and Diffusion Approximation Schemes.
7: Logistic Growth Models. 7.1. Deterministic Logistic Growth Model. 7.2. Shastic 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 Deviations of Logistic Growth Model in Random Media. 7.7. Shastic Stability of Logistic Growth Model in Averaging and Diffusion Approximation Schemes.
8: Predator-Prey Models. 8.1. Deterministic Predator-Prey Model. 8.2. Shastic Predator-Prey Model (Predator-Prey Model in Random Media). 8.3. Averaging of Predator-Prey Model in Random Media. 8.4. Merging of Predator-Prey Model. 8.5. Diffusion Approximation of Predator-Prey Model. 8.6. Normal Deviations of Predator-Prey Model in Random Media. 8.7. Shastic Stability of Predator-Prey Model in Averaging and Diffusion Approximation Schemes.
Bibliography. Index.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)