From one dimensional diffusions to symmetric Markov processes
From one dimensional diffusions to symmetric Markov processes
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DOI：
10.1016/j.spa.2010.01.010
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发表时间：
2010-05
影响因子：
1.4
通讯作者：
M. Fukushima
中科院分区：
文献类型：
--
作者：
M. Fukushima
对于一维正则区间I上的吸收扩散X 0，利用X 0的正则尺度s，给出了X 0在L2（I;m）及其扩展Dirichlet空间上的Dirichlet形式，其中m是X 0的正则测度.所有可能的对称扩展的X 0将被认为是与积极的反射狄利克雷空间的X 0。此外，对高维特殊扩散的可能对称扩展也作了类似的考虑，即在Rd，d≥3的闭区域上的时变瞬态反射布朗运动，它具有两个无穷锥分支.
For an absorbing diffusion X0on a one dimensional regular interval I with no killing inside, the Dirichlet form of X0on L2(I;m) and its extended Dirichlet space are identified in terms of the canonical scale s of X0, where m is the canonical measure of X0. All possible symmetric extensions of X0will then be considered in relation to the active reflected Dirichlet space of X0. Furthermore quite analogous considerations will be made for possible symmetric extensions of a specific diffusion in a higher dimension, namely, a time changed transient reflecting Brownian motion on a closed domain of Rd,d≥3, possessing two branches of infinite cones.