Related papers: A stochastic comparison result for the multitype c…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
A very classical problem in statistics is to test the stochastic superiority of one distribution to another. However, many existing approaches are developed for independent samples and, moreover, do not take censored data into account. We…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…
We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter…
We consider the cell population dynamics with $n$ different phenotypes. Both the Markovian branching process model (stochastic model) and the ordinary differential equation (ODE) system model (deterministic model) are presented, and…
We consider a system of stochastic interacting particles with general diffusion coefficient and drift functions and we study the types of collisions that arise in them. In particular, interactions between particles are inversely…
We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of…
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…
Multiple species in the ecosystem are believed to compete cyclically for survival and thus maintain balance in nature. Stochasticity has also an inevitable role in this dynamics. Considering these attributes of nature, the stochastic…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…
In a multitype branching process, it is assumed that immigrants arrive according to a nonhomogeneous Poisson or a generalized Polya process (both processes are formulated as a nonhomogeneous birth process with an appropriate choice of…
In a famous paper, Bezuidenhout and Grimmett demonstrated that the contact process dies out at the critical point.Their proof technique has often been used to study the growth of population patterns. The present text is intended as an…
We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the…
In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling…
A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…