Markov Evolution of Continuum Particle Systems with Dispersion and   Competition
  We construct birth-and-death Markov evolution of states(distributions) of point particle systems in $\mathbb{R}^d$. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other (compete). The main result is a statement that the corresponding correlation functions evolve in a scale of Banach spaces and remain sub-Poissonian, and hence no clustering occurs, if the dispersion is subordinate to the competition. 
Dmitri Finkelshtein, Yuri Kondratiev, Yuri Kozitsky, Oleksandr Kutoviy
math-ph math.DS math.MP math.PR