论文标题
具有渐近零漂移的一维马尔可夫链的强烈瞬态
Strong transience for one-dimensional Markov chains with asymptotically zero drifts
论文作者
论文摘要
对于莱米蒂（Lamperti）政权中非负整数上的近乎临界的瞬态马尔可夫链，$ x $的平均漂移为$ 1/x $ as $ x $ as $ x \ to \ infty $，我们可以通过存在条件返回时间和最后一次递增的递增时间来量化瞬时的瞬间，假设递增时间是统一的。我们的证明使用DOOB $ H $转换，用于暂时返回的瞬态过程，我们证明条件过程也是具有适当转换参数的Lamperti类型。为此，我们获得了两个回报概率比率的渐近扩展，在附近的两个起点处进行了评估。结果是，瞬态灯泡过程的返回概率是起点的常规变化函数。
For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return times and for last exit times, assuming increments are uniformly bounded. Our proof uses a Doob $h$-transform, for the transient process conditioned to return, and we show that the conditioned process is also of Lamperti type with appropriately transformed parameters. To do so, we obtain an asymptotic expansion for the ratio of two return probabilities, evaluated at two nearby starting points; a consequence of this is that the return probability for the transient Lamperti process is a regularly-varying function of the starting point.
