Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited
In this paper, polynomial recurrence bounds for a class of stochastic differential equations with a rotational symmetric gradient type drift and an additive Wiener process are established, as well as certain a priori moment inequalities for solutions. The key feature of this paper is that the approa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/14/3096 |
| _version_ | 1797588458459365376 |
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| author | Alexander Veretennikov |
| author_facet | Alexander Veretennikov |
| author_sort | Alexander Veretennikov |
| collection | DOAJ |
| description | In this paper, polynomial recurrence bounds for a class of stochastic differential equations with a rotational symmetric gradient type drift and an additive Wiener process are established, as well as certain a priori moment inequalities for solutions. The key feature of this paper is that the approach does not use Lyapunov functions because it is not clear how to construct them. The method based on Dynkin’s (nonrandom) chain of equations is applied instead. Another key feature is that the asymptotic conditions on the potential near infinity are assumed as inequalities—which allows for more flexibility compared to a single limit at infinity, making it less restrictive. |
| first_indexed | 2024-03-11T00:52:21Z |
| format | Article |
| id | doaj.art-edfa9c230aaa49148fd963e8b645dd77 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:52:21Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-edfa9c230aaa49148fd963e8b645dd772023-11-18T20:20:29ZengMDPI AGMathematics2227-73902023-07-011114309610.3390/math11143096Polynomial Recurrence for SDEs with a Gradient-Type Drift, RevisitedAlexander Veretennikov0Kharkevich Institute for Information Transmission Problems, Moscow 127051, RussiaIn this paper, polynomial recurrence bounds for a class of stochastic differential equations with a rotational symmetric gradient type drift and an additive Wiener process are established, as well as certain a priori moment inequalities for solutions. The key feature of this paper is that the approach does not use Lyapunov functions because it is not clear how to construct them. The method based on Dynkin’s (nonrandom) chain of equations is applied instead. Another key feature is that the asymptotic conditions on the potential near infinity are assumed as inequalities—which allows for more flexibility compared to a single limit at infinity, making it less restrictive.https://www.mdpi.com/2227-7390/11/14/3096stochastic differential equationsgradient type driftpolynomial recurrence |
| spellingShingle | Alexander Veretennikov Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited Mathematics stochastic differential equations gradient type drift polynomial recurrence |
| title | Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited |
| title_full | Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited |
| title_fullStr | Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited |
| title_full_unstemmed | Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited |
| title_short | Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited |
| title_sort | polynomial recurrence for sdes with a gradient type drift revisited |
| topic | stochastic differential equations gradient type drift polynomial recurrence |
| url | https://www.mdpi.com/2227-7390/11/14/3096 |
| work_keys_str_mv | AT alexanderveretennikov polynomialrecurrenceforsdeswithagradienttypedriftrevisited |