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Lipschitz-continuity of the integrated density of states for Gaussian random potentials
Lipschitz-continuity integrated density states for Gaussian random potentials
2011/1/17
The integrated density of states of a Schr¨odinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive me...
作者讨论非Lipschitz条件下g上鞅的非线性DoobMeyer 分解. 为此讨论一类漂移系数g(s,·,·)关于(y,z)不满足Lipschitz条件的倒向随机微分方程解的存在唯一性,运用Biharis不等式证明了一类倒向随机微分方程的比较定理以及g上解的极限定理.
本文研究如下形式的无穷维空间的倒向半线性随机发展方程
$$
x(t)+\int_t^T e^{A(s-t)}f(s,x(s),y(s))\, \d s+\int_t^T
e^{A(s-t)}[g(s,x(s))+y(s)]\, \d w(s)=e^{A(T-t)}X.
$$
在系数$f(t,x,y)$, $g(t,x)$满足一类非Lipschitz条件下得到了方程局部与整体适应解的存在唯...