Space-time dependence dynamics for birth-death point processes
Two examples of random point fields on \(\mathbb{R}^2\), depending on time, are considered. In both cases evolution of the field arises due to birth new points-offsprings and their dispersion along the plane or due to death of points. In the first example evolution of every point is independent of evolutions of other points of the field. In the second example the authors claim to take into account interaction of points in every time section. They assume the quantity and dispersion of offsprings of a point depend on a set of points belonging into \(R\)-neighborhood of this point. Some formulae for size of population as a function of birth and death coefficients are presented. Unfortunately the article is written insufficiently correctly (for example, they do not differ between random value and its expectation). Thus it is difficult to understand this paper.
scientific article; zbMATH DE number 5366057