The First Hitting Time of A Single Point for Random Walks

作者：Uchiyama Kohei^*

来源：Electronic Journal of Probability, 2011, 16: 1960-2000.

• hitting time
• asymptotic expansion
• Fourier analysis
• random walk

This paper concerns the first hitting time tau(0) of the origin for random walks on d-dimensional integer lattice with zero mean and a finite 2 + delta absolute moment (delta >= 0). We derive detailed asymptotic estimates of the probabilities P(x) [tau(0) = n] as n -> infinity that are valid uniformly in x, the position at which the random walks start

• 出版日期2011-10-21