Related papers: Critical Controlled Branching Processes and Their …
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that…
The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We investigate subcritical Galton-Watson branching processes with immigration in a random environment. Using Goldie's implicit renewal theory we show that under general Cram\'er condition the stationary distribution has a power law tail. We…
Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in random environment and let $\left\{ S_{n},n=0,1,2,...\right\} $ be its associated random walk. It is known that if the increments of this random walk belong…
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class…
The decomposable branching processes are relatively less studied objects, particularly in the continuous time framework. In this paper, we consider various variants of decomposable continuous time branching processes. As usual practice in…
Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what…
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice…
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
Given a discrete spatial structure $X$, we define continuous-time branching processes that model a population breeding and dying on $X$. These processes are usually called branching random walks. They are characterized by breeding rates…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…
Roughly speaking, clustering evolving networks aims at detecting structurally dense subgroups in networks that evolve over time. This implies that the subgroups we seek for also evolve, which results in many additional tasks compared to…