Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise
By constructing a coupling with unbounded time-dependent drift, a lower bound estimate of dimension-free Harnack inequality with power is obtained for a large class of stochastic differential equation with multiplicative noise. The key is an application of the inverse Hölder inequality. Combining th...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/5464688 |
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| _version_ | 1832555204679041024 |
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| author | Zihao An Gaofeng Zong |
| author_facet | Zihao An Gaofeng Zong |
| author_sort | Zihao An |
| collection | DOAJ |
| description | By constructing a coupling with unbounded time-dependent drift, a lower bound estimate of dimension-free Harnack inequality with power is obtained for a large class of stochastic differential equation with multiplicative noise. The key is an application of the inverse Hölder inequality. Combining this with the well-known upper bound, bilateral dimension-free Harnack inequality with power is established. As a dual inequality, the bilateral shift-Harnack inequalities with power are also investigated for stochastic differential equation with additive noise. Applications to the study of heat kernel inequalities are provided to illustrate the obtained inequalities. |
| format | Article |
| id | doaj-art-cce6470fa99043289ebd0efbb8e63fb5 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-cce6470fa99043289ebd0efbb8e63fb52025-02-03T05:49:25ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/5464688Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative NoiseZihao An0Gaofeng Zong1School of ScienceSchool of Statistics and MathematicsBy constructing a coupling with unbounded time-dependent drift, a lower bound estimate of dimension-free Harnack inequality with power is obtained for a large class of stochastic differential equation with multiplicative noise. The key is an application of the inverse Hölder inequality. Combining this with the well-known upper bound, bilateral dimension-free Harnack inequality with power is established. As a dual inequality, the bilateral shift-Harnack inequalities with power are also investigated for stochastic differential equation with additive noise. Applications to the study of heat kernel inequalities are provided to illustrate the obtained inequalities.http://dx.doi.org/10.1155/2022/5464688 |
| spellingShingle | Zihao An Gaofeng Zong Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise Journal of Function Spaces |
| title | Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise |
| title_full | Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise |
| title_fullStr | Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise |
| title_full_unstemmed | Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise |
| title_short | Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise |
| title_sort | bilateral harnack inequalities for stochastic differential equation with multiplicative noise |
| url | http://dx.doi.org/10.1155/2022/5464688 |
| work_keys_str_mv | AT zihaoan bilateralharnackinequalitiesforstochasticdifferentialequationwithmultiplicativenoise AT gaofengzong bilateralharnackinequalitiesforstochasticdifferentialequationwithmultiplicativenoise |