A note on almost sure exponential stability of θ-Euler-Maruyama approximation for neutral stochastic differential equations with time-dependent delay when θ ∈ (


12
{1 \over 2}

, 1)

Maja Obradović; Marija Milošević

doi:10.2478/auom-2024-0032

$A note on almost sure exponential stability of θ-Euler-Maruyama approximation for neutral stochastic differential equations with time-dependent delay when θ ∈ ( 12 {1 \over 2} , 1) Cover$

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A note on almost sure exponential stability of θ-Euler-Maruyama approximation for neutral stochastic differential equations with time-dependent delay when θ ∈ ( 12 {1 \over 2} , 1)

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 32 (2024): Issue 3 (October 2024)

By: Maja Obradović and Marija Milošević

Open Access

|Oct 2024

Abstract

This paper is motivated by the paper [2]. The main aim of this paper is to extend the stability result from [16], related to the θ-Euler- Maruyama method (θ ∈ ( $\frac{1}{2}$ {1 \over 2} , 1)) for a class of neutral stochastic differential equations with time-dependent delay. The theta method is defined such that, in general case, it is implicit in both drift coefficient and neutral term. Sufficient conditions of the a.s. exponential stability of the θ-Euler-Maruyama method, including the linear growth condition on the drift coefficient of the equation, are revealed. The stability result is established for larger class of neutral terms than that considered in the second cited paper. An example is provided to support the main results of the paper.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2024-0032 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 125 - 148

Submitted on: Sep 12, 2023

Accepted on: Dec 20, 2023

Published on: Oct 17, 2024

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

θ-Euler-Maruyama method,

Neutral stochastic differential equations,

Time-dependent delay,

Almost sure exponential stability,

Khasminskii-type condition

Related subjects:

Mathematics,

General mathematics

© 2024 Maja Obradović, Marija Milošević, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 32 (2024): Issue 3 (October 2024)