Weak order in averaging principle for stochastic differential equations with jumps
Abstract In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale parameter. We prove that the rate of weak convergence to the averaged dynamics is o...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-05-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1638-3 |
| _version_ | 1818216104458190848 |
|---|---|
| author | Bengong Zhang Hongbo Fu Li Wan Jicheng Liu |
| author_facet | Bengong Zhang Hongbo Fu Li Wan Jicheng Liu |
| author_sort | Bengong Zhang |
| collection | DOAJ |
| description | Abstract In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale parameter. We prove that the rate of weak convergence to the averaged dynamics is of order 1. This reveals that the rate of weak convergence is essentially twice that of strong convergence. |
| first_indexed | 2024-12-12T06:46:40Z |
| format | Article |
| id | doaj.art-5b5b6758b35d4b4685825da18d4e37ce |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T06:46:40Z |
| publishDate | 2018-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-5b5b6758b35d4b4685825da18d4e37ce2022-12-22T00:34:11ZengSpringerOpenAdvances in Difference Equations1687-18472018-05-012018112010.1186/s13662-018-1638-3Weak order in averaging principle for stochastic differential equations with jumpsBengong Zhang0Hongbo Fu1Li Wan2Jicheng Liu3College of Mathematics and Computer Science, Wuhan Textile UniversityCollege of Mathematics and Computer Science, Wuhan Textile UniversityCollege of Mathematics and Computer Science, Wuhan Textile UniversitySchool of Mathematics and Statistics, Huazhong University of Science and TechnologyAbstract In this paper, we deal with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equations. Under suitable conditions, we expand the weak error in powers of timescale parameter. We prove that the rate of weak convergence to the averaged dynamics is of order 1. This reveals that the rate of weak convergence is essentially twice that of strong convergence.http://link.springer.com/article/10.1186/s13662-018-1638-3Jump-diffusionAveraging principleInvariant measureWeak convergenceAsymptotic expansion |
| spellingShingle | Bengong Zhang Hongbo Fu Li Wan Jicheng Liu Weak order in averaging principle for stochastic differential equations with jumps Advances in Difference Equations Jump-diffusion Averaging principle Invariant measure Weak convergence Asymptotic expansion |
| title | Weak order in averaging principle for stochastic differential equations with jumps |
| title_full | Weak order in averaging principle for stochastic differential equations with jumps |
| title_fullStr | Weak order in averaging principle for stochastic differential equations with jumps |
| title_full_unstemmed | Weak order in averaging principle for stochastic differential equations with jumps |
| title_short | Weak order in averaging principle for stochastic differential equations with jumps |
| title_sort | weak order in averaging principle for stochastic differential equations with jumps |
| topic | Jump-diffusion Averaging principle Invariant measure Weak convergence Asymptotic expansion |
| url | http://link.springer.com/article/10.1186/s13662-018-1638-3 |
| work_keys_str_mv | AT bengongzhang weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps AT hongbofu weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps AT liwan weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps AT jichengliu weakorderinaveragingprincipleforstochasticdifferentialequationswithjumps |