Home Page Icon
Home Page
Table of Contents for
List of Notations
Close
List of Notations
by Vladimir Vatutin, Götz Kersting
Discrete Time Branching Processes in Random Environment
Cover
Title
Copyright
Preface
List of Notations
1 Branching Processes in Varying Environment
1.1. Introduction
1.2. Extinction probabilities
1.3. Almost sure convergence
1.4. Family trees
1.5. Notes
2 Branching Processes in Random Environment
2.1. Introduction
2.2. Extinction probabilities
2.3. Exponential growth in the supercritical case
2.4. Three subcritical regimes
2.5. The strictly critical case
2.6. Notes
3 Large Deviations for BPREs
3.1. Introduction
3.2. A tail estimate for branching processes in a varying environment
3.3. Proof of Theorem 3.1
3.4. Notes
4 Properties of Random Walks
4.1. Introduction
4.2. Sparre-Andersen identities
4.3. Spitzer identity
4.4. Applications of Sparre-Andersen and Spitzer identities
4.5. Notes
5 Critical BPREs: the Annealed Approach
5.1. Introduction
5.2. Changes of measures
5.3. Properties of the prospective minima
5.4. Survival probability
5.5. Limit theorems for the critical case (annealed approach)
5.6. Environment providing survival
5.7. Convergence of log Zn
5.8. Notes
6 Critical BPREs: the Quenched Approach
6.1. Introduction
6.2. Changes of measures
6.3. Probability of survival
6.4. Yaglom limit theorems
6.5. Discrete limit distributions
6.6. Notes
7 Weakly Subcritical BPREs
7.1. Introduction
7.2. The probability measures and
7.3. Proof of theorems
7.4. Notes
8 Intermediate Subcritical BPREs
8.1. Introduction
8.2. Proof of Theorems 8.1 to 8.3
8.3. Further limit results
8.4. Conditioned family trees
8.5. Proof of Theorem 8.4
8.6. Notes
9 Strongly Subcritical BPREs
9.1. Introduction
9.2. Survival probability and Yaglom-type limit theorems
9.3. Environments providing survival and dynamics of the population size
9.4. Notes
10 Multi-type BPREs
10.1. Introduction
10.2. Supercritical MBPREs
10.3. The survival probability of subcritical and critical MBPREs
10.4. Functional limit theorem in the critical case
10.5. Subcritical multi-type case
Appendix
A.1. Examples of slowly varying functions
Bibliography
Index
End User License Agreement
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Prev
Previous Chapter
Preface
Next
Next Chapter
1 Branching Processes in Varying Environment
List of Notations
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset
