Quasi-stationary simulation of the contact process

Quasi-stationary simulation of the contact process

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 interparticle gap-length distribution in the critical one-dimensional contact process. We also find evidence for power-law decay of the interparticle distance distri...

Quasi-Stationary Simulation: the Subcritical Contact Process

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate o...

The advantage of being slow: The quasi-neutral contact process

According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which mechanisms confer an advantage to a given species against the other(s)? In general, it is expected that the species with the higher reproductive/death ratio will...

Stationary Distribution of a Perturbed Quasi-birth-and-death Process

The Stationary - NonStationary Process and The Variable Roots Difference Equations

Stochastic, processes can be stationary or nonstationary. They depend on the magnitude of shocks. In other words, in an auto regressive model of order one, the estimated coefficient is not constant. Another finding of this paper is the relation between estimated coefficients and residuals. We also develop a catastrophe and chaos theory for change of roots from stationary to a nonstationary one ...