On the Euler–Maruyama Scheme for Degenerate Stochastic Differential Equations with Non-sticky Condition

Abstract

The aim of this paper is to study weak and strong convergence of the Euler-Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation dXt = σ(Xt)dWt with non-sticky condition. For proving this, we first prove that the Euler-Maruyama scheme also satisfies non-sticky condition. As an example, we consider stochastic differential equation dXt = |Xt| α dWt, α ∈ (0, 1/2) with non-sticky boundary condition and we give some remarks on CEV models in mathematical finance.