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We study discretizations of fractional fully nonlinear equations by powers ofdiscrete Laplacians. Our problems are parabolic and of order $\sigma\in(0,2)$since they involve fractional Laplace operators $(-\Delta)^{\sigma/2}$. Theyarise e.g.~in control and game theory as dynamic programming equations, andsolutions are non-smooth in general and should be interpreted as viscositysolutions. Our approximations are realized as finite-difference quadratureapproximations and are 2nd order accurate for all values of $\sigma$. Theaccuracy of previous approximations depend on $\sigma$ and are worse when$\sigma$ is close to $2$. We show that the schemes are monotone, consistent,$L^\infty$-stable, and convergent using a priori estimates, viscosity solutionstheory, and the method of half-relaxed limits. We present several numericalexamples.

Discretization of fractional fully nonlinear equations by powers of discrete Laplacians