2017/11/24 by Jesper Møller, Møller, Jesper, Andreas D. Christoffersen +1
Mathematics · #60D05 #60G55 #60J20 #62M30 #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1711.08984
openalex publication_date 2017/11/24 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We consider a Markov chain of point processes such that each state is a super\nposition of an independent cluster process with the previous state as its\ncentre process together with some independent noise process. The model extends\nearlier work by Felsenstein and Shimatani describing a reproducing population.\nWe discuss when closed term expressions of the first and second order moments\nare available for a given state. In a special case it is known that the pair\ncorrelation function for these type of point processes converges as the Markov\nchain progresses, but it has not been shown whether the Markov chain has an\nequilibrium distribution with this, particular, pair correlation function and\nhow it may be constructed. Assuming the same reproducing system, we construct\nan equilibrium distribution by a coupling argument.\n