Comparison principle for stochastic heat equations driven by α-stable white noises
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Bibliographic record
Abstract
For a class of non-linear stochastic heat equations driven by α-stable white noises for α∈(1,2) with Lipschitz coefficients, we prove the existence and pathwise uniqueness of Lp-valued càdlàg solution to such an equation for p∈(α,2] by considering a sequence of approximating stochastic heat equations driven by truncated α-stable white noises obtained by removing the big jumps from the original α-stable white noise. If the α-stable white noise is spectrally one-sided, under additional monotonicity assumption on noise coefficients, we further prove a comparison theorem on the L2-valued càdlàg solutions to such an equation. As a consequence, the non-negativity of the L2-valued càdlàg solution is established for the above stochastic heat equation with non-negative initial function.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.000 |
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| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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