Asymptotics and spectral results for random walks on p-adics-猫眼课题宝

p-adics 上随机游走的渐近和谱结果

DOI：

10.1016/s0304-4149(99)00016-2

发表时间：

1999

期刊：

Stochastic Processes and their Applications

影响因子：

1.4

通讯作者：

中科院分区：

数学3区

文献类型：

作者：

S. Albeverio;W. Karwowski;Xuelei Zhao

Markov semigroups on the field Qpof p-adic numbers which are symmetric with respect to a measure ρ(x) d x absolutely continuous relative to the Haar measure dx on Qpare constructed. The corresponding Dirichlet forms and associated Markov processes are exhibited and shown to be of the jump type. A detailed description of the spectrum of the generator (eigenvalues and eigenfunctions) is provided. Necessary and sufficient conditions for reducibility, recurrence and transience are found. Results about exit times from balls are also presented, as well as a proof of null recurrence.