论文标题
随机步行，在金字塔内漂移：生存概率的收敛速率
Random walks with drift inside a pyramid: convergence rate for the survival probability
论文作者
论文摘要
我们考虑在金字塔中进行多维随机步行，根据定义，这是由半空间的有限相交形成的锥体。感兴趣的主要对象是生存概率$ \ mathbb {p}（τ> n）$，$τ$，表示从固定金字塔中的第一个退出时间。当漂移属于锥体的内部时，生存概率序列会收敛到非EXIT概率$ \ Mathbb {p}（τ= \ infty）$，这是正的。在本说明中，我们量化了收敛速度，并证明可以通过随机步行增量的拉普拉斯变换的一定最小值来计算收敛速率。我们用各种示例来说明结果。
We consider multidimensional random walks in pyramids, which by definition are cones formed by finite intersections of half-spaces. The main object of interest is the survival probability $\mathbb{P}(τ>n)$, $τ$ denoting the first exit time from a fixed pyramid. When the drift belongs to the interior of the cone, the survival probability sequence converges to the non-exit probability $\mathbb{P}(τ=\infty)$, which is positive. In this note, we quantify the speed of convergence, and prove that the exponential rate of convergence may be computed by means of a certain min-max of the Laplace transform of the random walk increments. We illustrate our results with various examples.
