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

Amr Abosenna; Ghada AlNemer; Boping Tian

doi:10.3390/math12132016

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

Amr Abosenna
, Ghada AlNemer
, Boping Tian^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology
Benha University
Princess Nourah Bint Abdulrahman University

Research output: Contribution to journal › Article › peer-review

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 (Formula presented.) 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.

Original language	English
Article number	2016
Journal	Mathematics
Volume	12
Issue number	13
DOIs	https://doi.org/10.3390/math12132016
State	Published - Jul 2024
Externally published	Yes

Keywords

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

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10.3390/math12132016

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title = "Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with L{\'e}vy Jumps",

abstract = "This paper addresses a stochastic pantograph model with L{\'e}vy 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 (Formula presented.) 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 = "L{\'e}vy jumps, almost sure polynomial stability, convergence rate, split-step theta method, stochastic pantograph models",

author = "Amr Abosenna and Ghada AlNemer and Boping Tian",

note = "Publisher Copyright: {\textcopyright} 2024 by the authors.",

year = "2024",

month = jul,

doi = "10.3390/math12132016",

language = "英语",

volume = "12",

journal = "Mathematics",

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AU - Abosenna, Amr

AU - AlNemer, Ghada

AU - Tian, Boping

PY - 2024/7

Y1 - 2024/7

N2 - 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 (Formula presented.) 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.

AB - 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 (Formula presented.) 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.

KW - Lévy jumps

KW - almost sure polynomial stability

KW - convergence rate

KW - split-step theta method

KW - stochastic pantograph models

UR - https://www.scopus.com/pages/publications/85198441527

U2 - 10.3390/math12132016

DO - 10.3390/math12132016

M3 - 文章

AN - SCOPUS:85198441527

SN - 2227-7390

VL - 12

JO - Mathematics

JF - Mathematics

IS - 13

M1 - 2016

ER -

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

Abstract

Keywords

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