Strong order one-half convergence of a coupled tamed Euler--Peano scheme for reflected stochastic differential equations with super-linearly growing coefficients

Abstract

We study strong numerical approximations for reflected stochastic differential equations in possibly unbounded convex domains with super-linearly growing drift and diffusion coefficients. Under a coupled monotonicity condition and polynomial local Lipschitz assumptions, we first establish the well-posedness of the reflected SDE and derive uniform moment bounds for its solution. We then introduce a coupled tamed Euler--Peano scheme, in which the drift and the squared diffusion coefficient are tamed by a common factor and the resulting Euler--Peano path is corrected through the Skorokhod problem. This common taming factor preserves the drift--diffusion coercivity structure and yields uniform moment estimates for the numerical solution. We prove strong convergence of order $1/2$ for both the constrained state process and the boundary regulator, thereby recovering the standard Euler-type strong order in this reflected setting. Numerical experiments for a reflected stochastic Ginzburg--Landau type system illustrate the constraint preservation of the scheme and support the theoretical convergence rate.

36 pages, 4 figures