Potential kernel for two-dimensional random walk
Potential kernel for two-dimensional random walk
复制标题
二维随机游走的势核
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
K. Uchiyama
中科院分区：
文献类型：
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作者：
Yasunari Fukai;K. Uchiyama
证明了整数格Z2上常返非周期随机游动的势核存在形式为（2π）的渐近展开|Q|-1 ln Q（x 2，-x 1）+ const +| X| U 1（ω x）+|X|-2 U 2（ω x）+.，哪里|Q|和Q（θ）分别是随机游动增量X的协方差矩阵的行列式和二次型，ω x = x/|X|而Uk（ω）是ω的光滑函数，|ω| = 1，假设X的所有矩都是有限的。根据X的矩给出了U1和U2的显式表示.
It is proved that the potential kernel of a recurrent, aperiodic random walk on the integer lattice Z 2 admits an asymptotic expansion of the form (2π√|Q| -1 ln Q(x 2 , -x 1) + const + |x|U 1 (ω x ) + |x| -2 U 2 (ω x ) +..., where |Q| and Q(θ) are, respectively, the determinant and the quadratic form of the covariance matrix of the increment X of the random walk, ω x = x/|x| and the U k (ω) are smooth functions of ω,|ω|= 1, provided that all the moments of X are finite. Explicit forms of U 1 and U 2 are given in terms of the moments of X.