Piecewise-deterministic Markov processes for spatio-temporal population dynamics
Piecewise-deterministic Markov processes (PDMP) are cadlag Markov processes made of deterministic motions punctuated by random jumps. Typical methodological studies of PDMPs concern asymptotic behaviour, simulation and estimation of PDMPs. PDMPs have been used in numerous application fields and have been mostly exploited to model temporal dynamics.
Spatio-temporal population dynamics is a vast topic, which is of particular interest in ecology and epidemiology, and can be considered at various scales, from the microscopic scale to the global scale. A huge diversity of modeling approaches has been proposed to represent spatio-temporal population dynamics. Among these approaches, one can identify some which are based on PDMPs. My presentation will deal with these PDMPs used to represent spatio-temporal population dynamics and the possible perspectives in this field.