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

Amr Abosenna, Ghada AlNemer and Boping Tian ()
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Amr Abosenna: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Ghada AlNemer: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Boping Tian: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2024, vol. 12, issue 13, 1-16

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 L ϱ ^ ( 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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