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Large deviation principles for first-order scalar conservation laws with stochastic forcing
Zhao Dong,
Jiang-lun Wu,
Rangrang Zhang,
Tusheng Zhang
The Annals of Applied Probability, Volume: 30, Issue: 1, Pages: 324 - 367
Swansea University Author: Jiang-lun Wu
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DOI (Published version): 10.1214/19-aap1503
Abstract
In this paper, we established the Freidlin-Wentzell type large deviation principles for first- order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order co...
| Published in: | The Annals of Applied Probability |
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| ISSN: | 1050-5164 2168-8737 |
| Published: |
Institute of Mathematical Statistics
Institute of Mathematical Statistics
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa48584 |
| Abstract: |
In this paper, we established the Freidlin-Wentzell type large deviation principles for first- order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conser- vation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach. |
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| Keywords: |
large deviations; first-order conservation laws; weak convergence approach; kinetic solution. |
| Issue: |
1 |
| Start Page: |
324 |
| End Page: |
367 |