Birth and death on a flow refers to a particle system on a Brownian flow. Particles are born in a point process and move on the flow subject to position-dependent killing. They die eventually and leave the flow. The particle process is a measure-valued Markov process tracking these motions. Its law depends on the distribution of births, the coefficients of the flow and the rate of killing. We treat asymptotic likelihood estimation of these parameters from chronicles of the particle process as observed over a long period of time.
"Asymptotic likelihood estimation from birth and death on a flow." Ann. Statist. 24 (3) 1161 - 1184, June 1996. https://doi.org/10.1214/aos/1032526962