When can environmental profile and emissions reductions be optimized independently of the pollutant level?

Consider a model for optimal timing of emissions reduction, trading off the cost of the reduction against the time-additive aggregate of environmental damage, the disutility from the pollutant stock M(t) the infrastructure contributes to. Intuitively, the optimal timing for an infinitesimal pollution source should reasonably not depend on its historical contribution to the stock, as this is negligible. Dropping the size assumption, we show how to reduce the minimization problem to one not depending on the history of M, under linear evolution and suitable linearity or additivity conditions on the damage functional. We employ a functional analysis framework which allows for delay equations, non-Markovian driving noise, a choice between discrete and continuous time, and a menu of integral concepts covering stochastic calculi less frequently used in resource and environmental economics. Examples are given under the common (Markovian Itô) stochastic analysis framework.