AI 中文总结
本文刻画了无正跳跃的马尔可夫可加过程的尺度算子，用于解决双侧退出问题并刻画势测度，证明基于局部时间类似物和退出系统。
AI 中文摘要
本文考虑马尔可夫可加过程（MAPs），其可加分量取值于实数集且没有正跳跃。具体地，我们假设调制器是 Feller 过程，在每个有界时间区间上仅有有限多次跳跃，且可加分量在每个有界时间区间上也仅有有限多次跳跃。对于此类 MAPs，我们刻画了相关的尺度算子，并利用它们解决双侧退出问题，该问题关注在事件发生之前首次进入某半直线的时间，以及刻画当可加分量退出区间时被杀死的过程的势测度。我们的证明依赖于局部时间类似物的性质、将它们与合适的核配对得到的退出系统的性质，以及将 $C_0$-半群推广到 $C_0$-群的结果。
英文摘要
In this paper, we consider Markov additive processes (MAPs) whose additive components are $\bR$-valued and have no positive jumps. Specifically, we assume that the modulators are Feller processes with only finitely many jumps on each bounded time interval and that the additive components also have only finitely many jumps on each bounded time interval. For such MAPs, we characterize the associated scale operators and use them to solve the two-sided exit problem, which concerns the first entrance time into one half-line on the event that it is reached before the other, and to characterize the potential measures of the processes killed when their additive components exit an interval. Our proofs rely on properties of analogues of local times, properties of the exit systems obtained by pairing them with suitable kernels, and results on the extension of $C_0$-semigroups to $C_0$-groups.
Comments33 pages
