| 书目名称 | Classical Potential Theory and Its Probabilistic Counterpart |
| 副标题 | Advanced Problems |
| 编辑 | J. L. Doob |
| 视频video | |
| 丛书名称 | Grundlehren der mathematischen Wissenschaften |
| 图书封面 |  |
| 描述 | Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject |
| 出版日期 | Book 1984 |
| 关键词 | Markov process; Martingale; Motion; Potential theory; Probability theory; Transition function |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4612-5208-5 |
| isbn_ebook | 978-1-4612-5208-5Series ISSN 0072-7830 Series E-ISSN 2196-9701 |
| issn_series | 0072-7830 |
| copyright | Springer-Verlag New York Inc. 1984 |
发表于 2025-3-21 17:23:30
