Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with Lévy Jumps

Abstract

This paper addresses a stochastic pantograph model with Lévy leaps where non-jump coefficients exceed linearity. The partially truncated split-step theta method is introduced and applied to the proposed model. The finite time Lϱ^(ϱ^≥2) convergence rate of the numerical scheme is obtained. Furthermore, the almost sure polynomial stability of the numerical scheme is investigated and numerical examples are presented to endorse the addressed theorems.

Keywords

• stochastic pantograph models
• Lévy jumps
• split-step theta method
• convergence rate
• almost sure polynomial stability