Related papers: Survival and coexistence for a multitype contact p…
We consider the contact process with infection rate $\lambda$ on $\mathbb{T}_n^d$, the $d$-ary tree of height $n$. We study the extinction time $\tau_{\mathbb{T}_n^d}$, that is, the random time it takes for the infection to disappear when…
We consider a contact process on $Z^d$ with two species that interact in a symbiotic manner. Each site can either be vacant or occupied by individuals of species $A$ and/or $B$. Multiple occupancy by the same species at a single site is…
In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite…
We consider a continuous time Markov process on $\mathbb{N}_0$ which can be interpreted as generalized alternating birth-death process in a non-autonomous random environment. Depending on the status of the environment the process either…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
The existence of a weak survival region is established for the anisotropic symmetric contact process on a homogeneous tree T_{2d} of degree 2d > 2: For parameter values in a certain connected region of positive Lebesgue measure, the…
We introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate \phi until…
In this paper, we consider the threshold-one contact process and the threshold-one voter model w/o spontaneous death on homogeneous trees $\mathbb{T}_d$, $d\ge 2$. Mainly inspired by the corresponding arguments for ordinary contact…
We consider a spatial stochastic model for a pathogen population growing inside a host that attempts to eliminate the pathogens through its immune system. The pathogen population is divided into different types. A pathogen can either…
There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…
This paper is concerned with the death-birth updating process. This model is an example of a spatial game in which players located on the~$d$-dimensional integer lattice are characterized by one of two possible strategies and update their…
In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of…
We study a contact process running in a random environment in $\mathbb {Z}^d$ where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by…
Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (noncompact) type space. Conditions are…
The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…
This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…
In this paper we are concerned with the contact process on the squared lattice. The contact process intuitively describes the spread of the infectious disease on a graph, where an infectious vertex becomes healthy at a constant rate while a…
We study a class of quantum Markov processes that, on the one hand, is inspired by the micromaser experiment in quantum optics and, on the other hand, by classical birth and death processes. We prove some general geometric properties and…