Generalized Second-Order Differential Operators, Corresponding Gap Diffusions and Superharmonic Transformations
Generalized Second-Order Differential Operators, Corresponding Gap Diffusions and Superharmonic Transformations
复制标题
广义二阶微分算子、对应能隙扩散和超谐波变换
DOI：
10.1002/mana.3211480102
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发表时间：
1990
影响因子：
1
通讯作者：
W. Schenk
中科院分区：
文献类型：
--
作者：
H. Langer;W. Schenk
在我们的注释[LS]中，对于具有有限寿命5的任意间隙扩散X，已经描述了过程g，该过程g是通过在6处的时间反转从X获得的。本文的目的是给出[L 6]定理1-3的完整证明，并建立有关广义二阶微分算子及其相应的间隙扩散的更多的分析结果.在或多或少特殊的情况下，这样的结果也可以在文献中找到，所以有时我们只是粗略地证明，如果他们接近已知的。设δ是一个递增连续函数，m，k是（0，l）上的非减函数，使得对于相应的测度，我们有suppkcsuppm。我们考虑由关系dD：f-fdk dm定义的算子A
In our note [LS] for an arbitrary gap diffusion X with finite life time 5 there has been described the process g, which is obtained from X by time reversal at 6. It is the aim of this paper to give complete proofs for the Theorems 1-3 of [L6] and to establish more related analytical results about generalized second-order differential operators and the corresponding gap diffusions. In more or less partic-ular situations such results can also be found in the literature, so sometimes we do only sketch the proofs if they are close to known ones. Let 8 be an increasing continuous and m, k be nondecreasing functions on (0, l), such that for the corresponding measures we have supp kcsupp m. We consider the operator A, defined by the relation dD: f-fdk dm