Solution representation formula and Hopf lemma to Pucci’s equation

We establish the existence of a viscosity subsolution along with its representation formula to the equation involving Pucci’s extremal operator Mλ,Λ+ with zero-𝑡ℎ order term. We use a method based on a <i>dynamic programming principle</i> presented by Denis et al. (Potential Analysis, <b>34</b>(2), (2010), 139–161). As an application of our solution representation formula, we prove the Hopf lemma for Mλ,Λ− with zero-𝑡ℎ order term. Our approach is based on stochastic calculus and probabilistic methods.