Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions
This paper focuses on McKean-Vlasov stochastic differential equations under local Lipschitz conditions. We first introduce the stochastic interacting particle system and prove the propagation of chaos. Then we establish a truncated stochastic theta scheme to approximate the interacting particle syst...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/15/2433 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849239764772847616 |
|---|---|
| author | Hongxia Chu Haiyan Yuan Quanxin Zhu |
| author_facet | Hongxia Chu Haiyan Yuan Quanxin Zhu |
| author_sort | Hongxia Chu |
| collection | DOAJ |
| description | This paper focuses on McKean-Vlasov stochastic differential equations under local Lipschitz conditions. We first introduce the stochastic interacting particle system and prove the propagation of chaos. Then we establish a truncated stochastic theta scheme to approximate the interacting particle system and obtain the strong convergence of the continuous-time truncated stochastic theta scheme to the non-interacting particle system. Furthermore, we study the asymptotical mean square stability of the interacting particle system and the truncated stochastic theta method. Finally, we give one numerical example to verify our theoretical results. |
| format | Article |
| id | doaj-art-d72fddb800b34decbf6c69836fcf9dcb |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d72fddb800b34decbf6c69836fcf9dcb2025-08-20T04:00:50ZengMDPI AGMathematics2227-73902025-07-011315243310.3390/math13152433Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz ConditionsHongxia Chu0Haiyan Yuan1Quanxin Zhu2School of Electrical and Information Engineering, Heilongjiang Institute of Technology, Harbin 150050, ChinaDepartment of Mathematics, Heilongjiang Institute of Technology, Harbin 150050, ChinaSchool of Mathematics and Statistics, Hunan Normal University, Changsha 410081, ChinaThis paper focuses on McKean-Vlasov stochastic differential equations under local Lipschitz conditions. We first introduce the stochastic interacting particle system and prove the propagation of chaos. Then we establish a truncated stochastic theta scheme to approximate the interacting particle system and obtain the strong convergence of the continuous-time truncated stochastic theta scheme to the non-interacting particle system. Furthermore, we study the asymptotical mean square stability of the interacting particle system and the truncated stochastic theta method. Finally, we give one numerical example to verify our theoretical results.https://www.mdpi.com/2227-7390/13/15/2433McKean-Vlasov stochastic differential equationWasserstein distancetruncated stochastic theta methodstrong convergenceasymptotical mean square stability |
| spellingShingle | Hongxia Chu Haiyan Yuan Quanxin Zhu Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions Mathematics McKean-Vlasov stochastic differential equation Wasserstein distance truncated stochastic theta method strong convergence asymptotical mean square stability |
| title | Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions |
| title_full | Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions |
| title_fullStr | Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions |
| title_full_unstemmed | Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions |
| title_short | Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions |
| title_sort | convergence and stability of the truncated stochastic theta method for mckean vlasov stochastic differential equations under local lipschitz conditions |
| topic | McKean-Vlasov stochastic differential equation Wasserstein distance truncated stochastic theta method strong convergence asymptotical mean square stability |
| url | https://www.mdpi.com/2227-7390/13/15/2433 |
| work_keys_str_mv | AT hongxiachu convergenceandstabilityofthetruncatedstochasticthetamethodformckeanvlasovstochasticdifferentialequationsunderlocallipschitzconditions AT haiyanyuan convergenceandstabilityofthetruncatedstochasticthetamethodformckeanvlasovstochasticdifferentialequationsunderlocallipschitzconditions AT quanxinzhu convergenceandstabilityofthetruncatedstochasticthetamethodformckeanvlasovstochasticdifferentialequationsunderlocallipschitzconditions |