A class of long-run average control problems of Lotka-Voltera systems in a stochastic environment.

Nguyen, Dang H.; Tran, Ky Q.; Tuong, Tran D.; Yin, George

This work is devoted to studying a class of biological control problems in a stochastic environment. Specifically, it focuses on stochastic Lotka-Voltera systems. Our effort is on treating average cost per unit time controlled diffusions. It is natural to use a vanishing discount argument. However, in contrast to the existing literature, neither the 'near-monotone' nor the 'stable' condition is satisfied in the current set up. In reference to one of our recent works, we divide the domain into two parts. In one sub-domain, the 'near-monotone' condition is satisfied, whereas in the other sub-domain, the 'stable' condition is satisfied. We then carefully work out the analysis in the two domains so as to obtain the desired optimal control.

HAMILTON-Jacobi-Bellman equation; INVARIANT measures; STOCHASTIC systems; DIFFUSION control; UNITS of time

Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, p1

2156-8472

Academic Journal

10.3934/mcrf.2023041