AI 中文总结
研究具有有限正漂移的随机游走在中间正则变化时间间隔处停止的情况，通过特定条件设定，证明Sₜ和Mₜ分布尾部渐近等价且由τ尾部决定，随机游走仅通过大数定律影响，明确了三者关系。
AI 中文摘要
我们考虑具有有限正漂移的随机游走{Sₙ}，它在具有中间正则变化分布的随机时间τ处停止。我们假设跳跃分布比重尾于τ的分布。在这些条件下，我们表明Sₜ和Mₜ = maxₖ₍ₜ Sₖ的分布尾部渐近等价，且由τ的尾部决定，而随机游走{Sₙ}仅通过大数定律起作用。
英文摘要
We consider a random walk $\{S_n\}$ with a finite positive drift that is stopped at a random time $τ$ having an intermediate regularly varying distribution. We assume that the jump distribution is lighter-tailed than the distribution of $τ$. Under these conditions, we show that the tails of the distributions of $S_τ$ and $M_τ = \max_{k\le τ} S_k$ are asymptotically equivalent and are determined by the tail of $τ$, while the random walk $\{S_n\}$ contributes only through the law of large numbers.
Comments21 pages
