A RESULT OF MEAN SQUARE EXPONENTIAL STABILITY FOR DIFFERENTIAL DELAY EQUATIONS WITH STOCHASTIC NOISE.

Authors

  • Nguyen Nhu Quan Department of Mathematics, Electric Power University

DOI:

https://doi.org/10.51453/2354-1431/2023/849

Keywords:

Stochastic differential equation; moment exponential stability; almost surely exponential stability.

Abstract

In the present paper, we aim to study of a class of nonlinear differential equations with stochastic noise. Firstly, we introduce the condition of local Lipschitz and a new non-linear growth condition. Then by applying Lyapunov function and semi-martingale convergence theorem, we prove that the stochastic system under consideration has a unique global solution. Additionally, we also investigate the exponential stability of the mean square.

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References

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[10] W. Schoutens, Lévy Processes in Finance: Pricing Financial Derivatives, Wiley, 2003

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Published

2023-12-19

How to Cite

Nguyễn Như, Q. (2023). A RESULT OF MEAN SQUARE EXPONENTIAL STABILITY FOR DIFFERENTIAL DELAY EQUATIONS WITH STOCHASTIC NOISE. SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY, 9(5). https://doi.org/10.51453/2354-1431/2023/849

Issue

Vol. 9 No. 5 (2023): Scientific Education

Section

Natural Science and Technology

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