论文标题
部分可观测时空混沌系统的无模型预测
Existence of weak solutions to stochastic heat equations driven by truncated $α$-stable white noises with non-Lipschitz coefficients
论文作者
论文摘要
我们考虑一类由$α$稳定的白色噪声驱动的随机热方程，$ 1 <α<2 $，噪声系数连续但不一定是Lipschitz且满足全球线性生长条件。我们证明了弱解的存在，在两个不同的空间中使用值，使用弱收敛参数对近似随机热方程的解决方案。对于$ 1 <α<2 $，弱解决方案是一个值得值的càdlàg工艺。但是，以$ 1 <α<5/3 $的价格，弱解决方案是一个càdlàg流程采用功能值，在这种情况下，我们进一步表明，$ l^p $ norm的均匀解决方案的均匀解决方案是有限的，而薄弱的解决方案在$ L^p $中是有限的，并且在$ l^p $中是有限的，并且在$ l^p $中均持续不断地使人相处，并且满足了流量的范围。
We consider a class of stochastic heat equations driven by truncated $α$-stable white noises for $1<α<2$ with noise coefficients that are continuous but not necessarily Lipschitz and satisfy globally linear growth conditions. We prove the existence of weak solution, taking values in two different spaces, to such an equation using a weak convergence argument on solutions to the approximating stochastic heat equations. For $1<α<2$ the weak solution is a measure-valued càdlàg process. However, for $1<α<5/3$ the weak solution is a càdlàg process taking function values, and in this case we further show that for $0<p<5/3$ the uniform $p$-th moment for $L^p$-norm of the weak solution is finite, and that the weak solution is uniformly stochastic continuous in $L^p$ sense and satisfies a flow property.
