The oscillating random walk
The oscillating random walk
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振荡随机游走
DOI：
10.1016/0304-4149(74)90010-6
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发表时间：
1974
影响因子：
1.4
通讯作者：
J. Kemperman
中科院分区：
文献类型：
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作者：
J. Kemperman
{Yn;n=0，1，...}表示取值于Rd的平稳马尔可夫链。只要过程停留在固定超平面E0的同一侧，它就表现为分别具有跳跃测度μ或ν的普通随机游动。因此，普通随机游走将是μ = ν的特殊情况。此外，过程Y ′n=| Y′n−1−Zn|（与theZnas i.i.d.真实的随机变量）可以被视为特殊情况。一般过程的Wiener-Hopf型方法进行了研究。对于许多感兴趣的量，得到了精确的公式。对于Yn是整值的特殊情形，建立了更新型条件，这些条件是常返的充要条件.
{Yn;n=0, 1, …} denotes a stationary Markov chain taking values inRd. As long as the process stays on the same side of a fixed hyperplaneE0, it behaves as an ordinary random walk with jump measure μ or ν, respectively. Thus ordinary random walk would be the special case μ = ν. Also the processY′n= |Y′n−1−Zn| (with theZnas i.i.d. real random varia bles) may be regarded as a special case. The general process is studied by a Wiener–Hopf type method. Exact formulae are obtained for many quantities of interest. For the special case that theYnare integral-valued, renewal type conditions are established which are necessary and sufficient for recurrence.