The Comparison Principle For Viscosity Solution Of Fully Nonlinear Elliptic Integro-differential Equation

In this paper, we investigate comparison principle for semicontinuous viscosity solutions of fully nonlinear elliptic equation with nonlocal intergro-differential item. This kind of equation is from diffusion process with jumps and has important application in stochastic control and finance mathematics.In this paper,we study the following three problems.Firstly, we investigate the Dirichlet problem's comparison principle on a bounded subset for this fully nonlinear intergro-differential equation, at the same time we must assume the measure in the intergro-differential item is absolute continuous. The second problem is the comparison principle on the full space. For the viscosity supsolution and subsolution v and u, we have the result u< u onthe condition that lim Finally, we investigate the compar-iaon principle for unbounded functions on the full space. When the equation's subsolution and supsolution u and v satisfy C is constant) and the proper assumptions of the equation and the measure, we proved the comparison principle.