Stochastic Taylor Methods for Stochastic Delay Differential Equations
This paper demonstrates a systematic derivation of high order numerical methods from stochastic Taylor expansion for solving stochastic delay differential equations (SDDEs) with a constant time lag, r > 0 . The stochastic Taylor expansion of SDDEs is truncated at certain terms to achieve the orde...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universiti Teknologi Malaysia
2013
|
| Subjects: | |
| Online Access: | http://umpir.ump.edu.my/id/eprint/13514/ http://umpir.ump.edu.my/id/eprint/13514/1/29.1c.241-251.pdf |
| _version_ | 1848819491821060096 |
|---|---|
| author | Norhayati, Rosli Arifah, Bahar Hoe, Yeak Su Haliza, Abdul Rahman |
| author_facet | Norhayati, Rosli Arifah, Bahar Hoe, Yeak Su Haliza, Abdul Rahman |
| author_sort | Norhayati, Rosli |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | This paper demonstrates a systematic derivation of high order numerical methods from stochastic Taylor expansion for solving stochastic delay differential equations (SDDEs) with a constant time lag, r > 0 . The stochastic Taylor expansion of SDDEs is truncated at certain terms to achieve the order of convergence of numerical methods for SDDEs. Three different numerical schemes of Euler method, Milstein scheme and stochastic Taylor method of order 1.5 have been derived. The performance of Euler method, Milstein scheme and stochastic Taylor method of order 1.5 are investigated in a simulation study. |
| first_indexed | 2025-11-15T01:54:24Z |
| format | Article |
| id | ump-13514 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T01:54:24Z |
| publishDate | 2013 |
| publisher | Universiti Teknologi Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-135142016-12-28T08:38:49Z http://umpir.ump.edu.my/id/eprint/13514/ Stochastic Taylor Methods for Stochastic Delay Differential Equations Norhayati, Rosli Arifah, Bahar Hoe, Yeak Su Haliza, Abdul Rahman QA Mathematics This paper demonstrates a systematic derivation of high order numerical methods from stochastic Taylor expansion for solving stochastic delay differential equations (SDDEs) with a constant time lag, r > 0 . The stochastic Taylor expansion of SDDEs is truncated at certain terms to achieve the order of convergence of numerical methods for SDDEs. Three different numerical schemes of Euler method, Milstein scheme and stochastic Taylor method of order 1.5 have been derived. The performance of Euler method, Milstein scheme and stochastic Taylor method of order 1.5 are investigated in a simulation study. Universiti Teknologi Malaysia 2013-06 Article PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/13514/1/29.1c.241-251.pdf Norhayati, Rosli and Arifah, Bahar and Hoe, Yeak Su and Haliza, Abdul Rahman (2013) Stochastic Taylor Methods for Stochastic Delay Differential Equations. MATEMATIKA, 29 (1c). pp. 241-251. ISSN 0127-8274. (Published) http://dx.doi.org/10.11113/matematika.v29.n.597 10.11113/matematika.v29.n.597 |
| spellingShingle | QA Mathematics Norhayati, Rosli Arifah, Bahar Hoe, Yeak Su Haliza, Abdul Rahman Stochastic Taylor Methods for Stochastic Delay Differential Equations |
| title | Stochastic Taylor Methods for Stochastic Delay Differential Equations |
| title_full | Stochastic Taylor Methods for Stochastic Delay Differential Equations |
| title_fullStr | Stochastic Taylor Methods for Stochastic Delay Differential Equations |
| title_full_unstemmed | Stochastic Taylor Methods for Stochastic Delay Differential Equations |
| title_short | Stochastic Taylor Methods for Stochastic Delay Differential Equations |
| title_sort | stochastic taylor methods for stochastic delay differential equations |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/13514/ http://umpir.ump.edu.my/id/eprint/13514/ http://umpir.ump.edu.my/id/eprint/13514/ http://umpir.ump.edu.my/id/eprint/13514/1/29.1c.241-251.pdf |