The fallow and the non-fallow states in swidden agriculture: a stochastic analysis

At any point in time, a cleared parcel of forest land (CPFL) used for swidden agriculture exists in either the fallow or in the non-fallow state. Further, the practice of swidden agriculture requires one to operate in an environment of uncertainty. These two points notwithstanding, there are virtually no probabilistic models of swidden agriculture that explicitly account for the above dichotomy. Hence, in this paper, we use a stochastic model and a long run perspective to shed light on two hitherto unstudied questions concerning a CPFL used for swidden agriculture. First, we use renewal theory to determine the long run fraction of time that our CPFL is in either the fallow or in the non-fallow state. Second, we use the hyperexponential distribution to compute the stationary probability that the excess variable associated with the stochastic process representing our CPFL exceeds a given value.