A monotone scheme for nonlinear partial integro-differential equations with the convergence rate of α-stable limit theorem under sublinear expectation
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In this paper, we propose a monotone approximation scheme for a class of fully nonlinear partial integro-differential equations (PIDEs) which characterize the nonlinear α-stable Lévy processes under sublinear expectation space with α∈(1,2). Two main results are obtained: (i) the error bounds for the monotone approximation scheme of nonlinear PIDEs, and (ii) the convergence rates of a generalized central limit theorem of Bayraktar-Munk for α-stable random variables under sublinear expectation. Our proofs use and extend techniques introduced by Krylov and Barles-Jakobsen.
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