A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models
In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special proper...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/6/588 |
| _version_ | 1797541969632690176 |
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| author | Yang Li Taitao Feng Yaolei Wang Yifei Xin |
| author_facet | Yang Li Taitao Feng Yaolei Wang Yifei Xin |
| author_sort | Yang Li |
| collection | DOAJ |
| description | In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results. |
| first_indexed | 2024-03-10T13:23:08Z |
| format | Article |
| id | doaj.art-52272c919b8e436f84df816b02b7badd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T13:23:08Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-52272c919b8e436f84df816b02b7badd2023-11-21T09:52:08ZengMDPI AGMathematics2227-73902021-03-019658810.3390/math9060588A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic ModelsYang Li0Taitao Feng1Yaolei Wang2Yifei Xin3College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaIn this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results.https://www.mdpi.com/2227-7390/9/6/588weak order 2.0 schememarkovian switchingmalliavin calculus |
| spellingShingle | Yang Li Taitao Feng Yaolei Wang Yifei Xin A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models Mathematics weak order 2.0 scheme markovian switching malliavin calculus |
| title | A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models |
| title_full | A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models |
| title_fullStr | A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models |
| title_full_unstemmed | A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models |
| title_short | A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models |
| title_sort | high order accurate and effective scheme for solving markovian switching stochastic models |
| topic | weak order 2.0 scheme markovian switching malliavin calculus |
| url | https://www.mdpi.com/2227-7390/9/6/588 |
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