论文标题
象限中瞬态反射过程的总统治的概率
Probability of total domination for transient reflecting processes in a quadrant
论文作者
论文摘要
我们认为反映在阳性象限中的二维lévy过程。当自由过程的平均值为负时，我们的重点是非标准制度，但是反射矢量远离原点，因此反射过程沿其中一个轴逃到了无穷大。在相当普遍的条件下，这表明这种行为是确定的，每个组件可以在任何给定的起始位置上以正概率为主导。此外，我们建立了相应的不变性原理，为使用反射的布朗运动作为近似模型提供了理由。为了关注第一个组件主导的概率，我们为起始位置中各个拉普拉斯变换的核方程提供了一个内核方程。这是针对具有负指数跳跃的复合泊松模型的，并且通过近似值，对于布朗模型。两个方程都是通过边界价值问题分析求解的，这在开始时也会产生统治概率。最后，提出了某些渐近分析和数值结果。
We consider two-dimensional Lévy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that the reflected process escapes to infinity along one of the axes. Under rather general conditions, it is shown that such behaviour is certain and each component can dominate the other with positive probability for any given starting position. Additionally, we establish the corresponding invariance principle providing justification for the use of the reflected Brownian motion as an approximate model. Focusing on the probability that the first component dominates, we derive a kernel equation for the respective Laplace transform in the starting position. This is done for the compound Poisson model with negative exponential jumps and, by means of approximation, for the Brownian model. Both equations are solved via boundary value problem analysis, which also yields the domination probability when starting at the origin. Finally, certain asymptotic analysis and numerical results are presented.
