Construction of continuous-state branching processes in varying environments
نویسندگان
چکیده
A continuous-state branching process in varying environments is constructed by the pathwise unique positive solution to a stochastic integral equation driven time-space noises. The cumulant semigroup of characterized terms backward equation. We clarify behavior at its bottlenecks, which are deterministic times when it arrives zero almost surely negative jumps. arises naturally as scaling limit Galton–Watson processes environments.
منابع مشابه
Resistance Dimensions of Branching Processes in Varying Environments Trees
In this paper we pursue our study, in [5] and [6], on dimensions of some random trees. These dimensions are, for polynomially growing graphs, closely related to the type (transience-recurrence) problem of the simple random walk on such graphs. We give an interval estimation for the mean resistance dimension of branching processes in varying environments trees.
متن کاملContinuous-state Branching Processes and Self-similarity
In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov process...
متن کاملLévy processes and continuous - state branching processes : part I
Let us begin by recalling the definition of two familiar processes, a Brownian motion and a Poisson process. A real-valued process B = {B t : t ≥ 0} defined on a probability space (Ω, F , P) is said to be a Brownian motion if the following hold: (i) The paths of B are P-almost surely continuous. (ii) P(B 0 = 0) = 1. (iii) For 0 ≤ s ≤ t, B t − B s is equal in distribution to B t−s. (iv) For 0 ≤ ...
متن کاملLévy processes and continuous-state branching processes: part III
Originating in part from the concerns of the Victorian British upper classes that aristocratic surnames were becoming extinct, the theory of branching processes now forms a cornerstone of classical applied probability. Some of the earliest work on branching processes dates back to Galton and Watson in 1874, [25]. However, approximately 100 years later, it was discovered in [13] that the less we...
متن کاملLévy processes and continuous-state branching processes: part II
In this section we discuss a simple feature of all Lévy processes which follows as a direct consequence of stationary independent increments. That is, when the path of a Lévy process over a finite time horizon is time reversed (in an appropriate sense) the new path is equal in law to the process reflected about the origin. This property will prove to be of crucial importance in a number of fluc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Applied Probability
سال: 2022
ISSN: ['1050-5164', '2168-8737']
DOI: https://doi.org/10.1214/21-aap1770