Estimates for Differences and Harnack Inequality for Difference Operators Coming From Random Walks with Symmetric, Spatially Inhomogeneous, Increments
Estimates for Differences and Harnack Inequality for Difference Operators Coming From Random Walks with Symmetric, Spatially Inhomogeneous, Increments
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来自具有对称、空间非均匀增量的随机游走的差分算子的差分和哈纳克不等式的估计
DOI：
10.1112/plms/s3-63.3.552
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发表时间：
1991
影响因子：
1.8
通讯作者：
G. Lawler
中科院分区：
文献类型：
--
作者：
G. Lawler
研究了具有对称增量的随机游动产生的差分算子。如果随机游动是空间齐次的，则给出了调和函数的一阶和二阶差的估计，并证明了一个Harnack不等式。在空间非齐次的情况下，证明了超调和函数的一个Harnack不等式，给出了Krylov和Safonov的一个结果的离散版本。给出了调和函数差的一个估计，并用它证明了空间非均匀游动的调和测度的存在性。
Difference operators arising from random walks with symmetric increments are studied. If the random walk is spatially homogeneous, then estimates of the first and second differences of harmonic functions are given and a Harnack inequality is proved. In the spatially inhomogeneous case, a Harnack inequality for superharmonic functions is proved, giving a discrete version of a result of Krylov and Safonov. This is used to give an estimate for differences of harmonic functions and applied to show existence of harmonic measure for spatially inhomogeneous walks.