论文标题
由$α$稳定的白色噪声驱动的随机热方程的比较原理
Comparison principle for stochastic heat equations driven by $α$-stable white noises
论文作者
论文摘要
对于一类由$α$稳定的白色噪声驱动的非线性随机热方程式，$α\ in（1,2）$带有Lipschitz系数，我们首先显示出$ l^p $ l^p $ v $ valuredcàdlàg解决方案的存在和路径的唯一性，该方程式通过$ p \ in（通过（通过$ p femive in）来进行$ p \ in of（a）的[limim p] y impive in（2），以α，2] $ a的传热率，截断 $α$ - 稳定的白色噪声是通过从原始$α$稳定的白色噪声中删除大跳来获得的。 如果在噪声系数上的额外单调假设下，$α$稳定的白噪声是单侧的，我们证明了对此类方程的$ l^2 $可值的càdlàg解决方案的比较定理。结果，为上述随机热方程式建立了$ l^2 $ - 价值的Càdlàg解决方案的非负性。
For a class of non-linear stochastic heat equations driven by $α$-stable white noises for $α\in(1,2)$ with Lipschitz coefficients, we first show the existence and pathwise uniqueness of $L^p$-valued càdlàg solutions to such a equation for $p\in(α,2]$ 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 noises. If the $α$-stable white noise is spectrally one-sided, under additional monotonicity assumption on noise coefficients, we prove a comparison theorem on the $L^2$-valued càdlàg solutions of such a equation. As a consequence, the non-negativity of the $L^2$-valued càdlàg solution is established for the above stochastic heat equation with non-negative initial function.
