An Introduction to the Theory of Large Deviations
An Introduction to the Theory of Large Deviations
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DOI：
10.1007/978-1-4613-8514-1
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
D. Stroock
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文献类型：
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作者：
D. Stroock
这些笔记是基于我1983-84学年在科罗拉多大学教授的一门课程。我的意图是为我的听众和我自己提供一个对变异理论的介绍·第1)至3)节的组织在某种程度上归功于偶然，并在很大程度上归功于R.Azencott为1978年在圣面粉(参见《斯普林格数学讲义》774)。更准确地说，施尔德撰写论文的时候，我恰好在纽约大学附近。因此，我选择使用他的结果作为起点，只是有很小的变化，这可能被认为是偶然的。这些区域的其他所有东西都是从阿森科特那里拿走的。尤其是。第三节)只不过是通过巴哈杜尔和扎贝尔的思想重写了他对克雷默理论的解释。更重要的是。我在第4节中对文塞尔-弗莱德林理论的简要论述也是基于阿森科特的思想。总而言之。他和我对这些主题的阐述最大的不同之处在于我们所用的语言。然而。另一个必须提到的主要区别是：他的参考书目很广泛，是对现有文献的很好的介绍。我的这两个属性都不同。从第5条开始)。
These notes are based on a course which I gave during the academic year 1983-84 at the University of Colorado. My intention was to provide both my audience as well as myself with an introduction to the theory of 1arie deviations• The organization of sections 1) through 3) owes something to chance and a great deal to the excellent set of notes written by R. Azencott for the course which he gave in 1978 at Saint-Flour (cf. Springer Lecture Notes in Mathematics 774). To be more precise: it is chance that I was around NYU at the time'when M. Schilder wrote his thesis. and so it may be considered chance that I chose to use his result as a jumping off point; with only minor variations. everything else in these sections is taken from Azencott. In particular. section 3) is little more than a rewrite of his exoposition of the Cramer theory via the ideas of Bahadur and Zabel. Furthermore. the brief treatment which I have given to the Ventsel-Freidlin theory in section 4) is again based on Azencott's ideas. All in all. the biggest difference between his and my exposition of these topics is the language in which we have written. However. another major difference must be mentioned: his bibliography is extensive and constitutes a fine introduction to the available literature. mine shares neither of these attributes. Starting with section 5).