منابع مشابه
Continuous-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 کاملOn the extinction of Continuous State Branching Processes with catastrophes
We consider continuous state branching processes (CSBP’s) with additional multiplicative jumps modeling dramatic events in a random environment. These jumps are described by a Lévy process with bounded variation paths. We construct the associated class of processes as the unique solution of a stochastic differential equation. The quenched branching property of the process allows us to derive qu...
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: Bulletin of the American Mathematical Society
سال: 1967
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1967-11762-2