ar X iv : 0 90 6 . 14 58 v 1 [ m at h . A P ] 8 J un 2 00 9 DIFFERENCE - QUADRATURE SCHEMES FOR NONLINEAR DEGENERATE PARABOLIC INTEGRO - PDE
نویسنده
چکیده
We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Lévy measures. Furthermore, we develop a new general theory for deriving error estimates for approximate solutions of integro-PDEs, which thereafter is applied to the proposed difference-quadrature schemes.
منابع مشابه
Difference-Quadrature Schemes for Nonlinear Degenerate Parabolic Integro-PDE
We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Lévy...
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