论文标题
跳跃过程的向左，向右和完整的退出时间分布
Leftward, Rightward and Complete Exit Time Distributions of Jump Processes
论文作者
论文摘要
很好地描述了以1维间隔限制的连续随机过程的第一通道特性。但是，对于跳跃过程（离散随机步行），尽管在各种情况下相关，但相应可观察物的表征仍然难以捉摸。在这里，我们从间隔$ [0，x] $的左，向右和完整退出时间分布中得出确切的渐近表达式，用于对称跳跃过程，从$ x_0 = 0 $开始，在大$ x $中，大$ x $和大的时间限制。我们表明，两个向左的概率$ f _ {\下划线{0}，x}（n）$要通过$ 0 $在步骤$ n $处出口，并且向右概率$ f_ {0，\ usever \ usever \ usever \ usever {x}}}}（n）$通过$ n $在$ n $上通过$ n $ yourcy $ n $ decrestion $ n $ dection $ decression the jumm deprestion the jumm depertion the jumm demite demitive of fe nemund off le jumm nive。特别是，我们详尽地描述了$ n \ ll x^μ$和$ n \ gg x^μ$限制，并在这两个制度中获得明确的结果。我们的结果最终为在不适用连续限制的方案中的跳跃过程的退出时间分布提供了确切的渐近学。
First-passage properties of continuous stochastic processes confined in a 1--dimensional interval are well described. However, for jump processes (discrete random walks), the characterization of the corresponding observables remains elusive, despite their relevance in various contexts. Here we derive exact asymptotic expressions for the leftward, rightward and complete exit time distributions from the interval $[0,x]$ for symmetric jump processes starting from $x_0=0$, in the large $x$ and large time limit. We show that both the leftward probability $F_{\underline{0},x}(n)$ to exit through $0$ at step $n$ and rightward probability $F_{0,\underline{x}}(n)$ to exit through $x$ at step $n$ exhibit a universal behavior dictated by the large distance decay of the jump distribution parameterized by the Levy exponent $μ$. In particular, we exhaustively describe the $n\ll x^μ$ and $n\gg x^μ$ limits and obtain explicit results in both regimes. Our results finally provide exact asymptotics for exit time distributions of jump processes in regimes where continuous limits do not apply.
