Strong convergence on a stochastic controlled Lotka-Volterra 3-species model with L´evy jumps

In this paper we study two properties of the numerical solutions a controlled stochastic Lotka-Volterra one-predator-two-prey model, namely boundedness in mean and strong convergence these solutions. We also establish solve, by means Stochastic Maximum Principle, corresponding optimal control problem population modeled system with types environmental fluctuations: white noise L´evy jumps. Our shows, assuming standard linear growth Lipschitz conditions on drift diffusion coefficients, that scheme are preserved model.