| 书目名称 | Excursions of Markov Processes |
| 编辑 | Robert M. Blumenthal |
| 视频video | |
| 丛书名称 | Probability and Its Applications |
| 图书封面 |  |
| 描述 | Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T < s < t. When one measures the time in t the zero set appropriately (in terms of the local time) the excursions acquire a measure theoretic structure practically identical to that of processes with stationary independent increments, except the values of the process are paths rather than real numbers. And there is a measure on path space that helps describe the measure theoretic properties of the excursions in the same way that the Levy measure describes the jumps of a process with independent increments. The entire circle of ideas is called excursion theory. There are many attractive things about the subject: it is an area where one can use to advantage general probabilistic potential theory to make quite specific calculations, it provides a natural setting for apply ing esoteric things like David Williams‘ path decomposition, it provides a method for constructing processes whose description in terms of an in finitesimal generato |
| 出版日期 | Textbook 1992 |
| 关键词 | Generator; Markov process; local time; path space; probability |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4684-9412-9 |
| isbn_softcover | 978-1-4684-9414-3 |
| isbn_ebook | 978-1-4684-9412-9Series ISSN 2297-0371 Series E-ISSN 2297-0398 |
| issn_series | 2297-0371 |
| copyright | Springer Science+Business Media New York 1992 |
发表于 2025-3-21 16:43:28
