Journal article 1283 views
Degenerate SDE with Hölder--Dini Drift and Non-Lipschitz Noise Coefficient
,
Xicheng Zhang
SIAM Journal on Mathematical Analysis, Volume: 48, Issue: 3, Pages: 2189 - 2226
Swansea University Author:
Feng-yu Wang
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DOI (Published version): 10.1137/15M1023671
Abstract
The existence-uniqueness and stability of strong solutions are proved for a class of degenerate stochastic differential equations, where the noise coefficient might be non-Lipschitz, and the drift is locally Dini continuous in the component with noise (i.e., the second component) and locally Hölder-...
| Published in: | SIAM Journal on Mathematical Analysis |
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| Published: |
2016
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa29740 |
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| Abstract: |
The existence-uniqueness and stability of strong solutions are proved for a class of degenerate stochastic differential equations, where the noise coefficient might be non-Lipschitz, and the drift is locally Dini continuous in the component with noise (i.e., the second component) and locally Hölder--Dini continuous of order $\frac{2}{3}$ in the first component. Moreover, the weak uniqueness is proved under weaker conditions on the noise coefficient. Furthermore, if the noise coefficient is $C^{1+\varepsilon}$ for some ${\varepsilon}>0$ and the drift is Hölder continuous of order ${\alpha}{\in} (\frac{2}{3},1)$ in the first component and order ${\beta\in}(0,1) $ in the second, the solution forms a $C^1$-stochastic diffeormorphism flow. To prove these results, we present some new characterizations of Hölder--Dini space by using the heat semigroup and slowly varying functions. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
3 |
| Start Page: |
2189 |
| End Page: |
2226 |