Log In Sign Up

A monotone scheme for nonlinear partial integro-differential equations with the convergence rate of α-stable limit theorem under sublinear expectation

by   Mingshang Hu, et al.

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.


page 1

page 2

page 3

page 4


Numerical Schemes for Backward Stochastic Differential Equations Driven by G-Brownian motion

We design a class of numerical schemes for backward stochastic different...

A Forward Propagation Algorithm for Online Optimization of Nonlinear Stochastic Differential Equations

Optimizing over the stationary distribution of stochastic differential e...

Green's function for singular fractional differential equations and applications

In this paper, we study the existence of positive solutions for nonlinea...

Variance-Reduced Proximal and Splitting Schemes for Monotone Stochastic Generalized Equations

We consider monotone inclusion problems where the operators may be expec...