关于随机游动转移函数性质的若干注记

SOME NOTES ON THE PROPERTIES OF THE TRANSITION FUNCTION OF A RANDOM WALK

本文讨论了随机游动的若干性质并得到了主要结果:对均值μ=0,具有限二阶矩的真d维随机游动。

Some properties of random walk are discussed. The main result is:For genuinely d-dimensional random walk with mean μ=0 and finite second moments. both hold uniformly for all x∈Z^d. where x_0 is a point satisfied P(0,x_0)>0, A is a d×d matrix with integral elements, such that {xA: x∈Z^d} is the additive group generated by {x:Q(0,x)>0}, Q(x,y)≡P(x,t) P(y,t), x, y∈Z^d,Q=x'xP(0,x), |Q|is the determinant of Q.