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Stochastic description of delayed systems

Lafuerza, Luis F.; Toral, Raul
Philosophical Transactions of the Royal Society A 371, 20120458 (2013)

We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with arbitrary probability distributions. The interplay between stochasticity and delay and, in particular, the effects of delay in the fluctuations and time correlations are discussed.