Branching processes with random environments
Krishna B. Athreya,Samuel Karlin +1 more
Reads0
Chats0
TLDR
In this article, the authors postulate that {Zn} satisfy the recurrence relations (5) E(s^\\Fn,z) = K W ] ^ a.s.Abstract:
We postulate that {Zn} satisfy the recurrence relations (5) E(s^\\Fn,z) = K W ] ^ a.s. and for any set of integers l ^ W i < w 2 < • • • <rik with | s t | â l , A MS Subject Classifications. Primary 6067; Secondary 6030.read more
Citations
More filters
Journal ArticleDOI
Conceptual proofs of L log L criteria for mean behavior of branching processes
TL;DR: The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an $L \log L$ condition is decisive as mentioned in this paper.
Journal ArticleDOI
Demographic and Environmental Stochasticity Concepts and Definitions
TL;DR: In this article, general definitions of demographic and environmental variances as well as demographic covariance are given from first principles, which are consistent with use of these terms in models with additive effects and in diffusion approximations to population processes.
Journal ArticleDOI
Ergodic theorems in demography
TL;DR: The strong and weak ergodic theorems of demography as mentioned in this paper describe the properties of a product of certain nonnegative matrices, in the limit as the number of matrix factors in the product becomes large.
Journal ArticleDOI
Random temporal variation in selection intensities: Case of large population size☆
TL;DR: This work presents the first study of a diploid model involving selection forces exhibiting systematic temporal variation and investigates the influence of random fluctuations in selection intensities on the growth behavior of haploid populations.
Journal ArticleDOI
From stochastic environments to life histories and back
TL;DR: This paper examines life-history evolution in a variable environment, by decomposing average individual fitness into contributions from average vital rates and their temporal variation, and shows that stochastic growth rates are strongly affected by demographic dispersion, even when deterministic growth rate rates are not.
References
More filters
Book
The Theory of Branching Processes
TL;DR: A review of the Galton and Watson mathematical model that applies probability theory to the effects of chance on the development of populations is given in this article, followed by a systematic development of branching processes, and a brief description of some of the important applications.
Journal ArticleDOI
A Limit Theorem for Multidimensional Galton-Watson Processes
Harry Kesten,B. P. Stigum +1 more
Journal ArticleDOI
On Branching Processes in Random Environments
TL;DR: In this article, the branching process of a Markov chain is defined as a branching process such that each point in the chain is associated with a variable associated with an operating system.
Related Papers (5)
On Branching Processes with Random Environments: I: Extinction Probabilities
Krishna B. Athreya,Samuel Karlin +1 more