Weak convergence of delay SDEs with applications to Carathéodory approximation

Ta Cong Son; Nguyen Tien Dung; Nguyen Van Tan; Tran Manh Cuong; Hoang Thi Phuong Thao; Pham Dinh Tung

doi:10.3934/dcdsb.2021249

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2022, Volume 27, Issue 9: 4725-4747. Doi: 10.3934/dcdsb.2021249

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Weak convergence of delay SDEs with applications to Carathéodory approximation

1.
Department of Mathematics, VNU University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, 084, Vietnam
2.
Department of Foundation, Academy of Cryptography Techniques, 141 Chien Thang, Thanh Tri, Hanoi, 084, Vietnam

^* Corresponding author: Nguyen Tien Dung
^* Corresponding author: Nguyen Tien Dung

Received: April 30, 2020

Revised: May 31, 2021

Early access: October 2021

Published: September 2022

N. T. Dung and H. T. P. Thao are supported by the Vietnam National University, Hanoi under grant number QG.20.21. T. C. Son, N. V. Tan, T. M. Cuong and P. D. Tung are supported by Viet Nam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2019.08

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Abstract

In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Carathéodory approximation scheme of stochastic differential equations is provided as well.

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Mathematics Subject Classification: Primary: 65C30, 60H10; Secondary: 60H07.

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References

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