Abstract
Martingales are probably the most ingenious invention and generalization of sums of independent random variables with mean 0. They play an important role in probability theory and in statistics. They are also extremely applicable, mathematically tractable, and astonishingly exploitable in purely mathematical contexts. In addition, the theory is extremely elegant and aesthetically appealing.
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Notes
- 1.
The term is also used in non-mathematical contexts, although the origin as well as the etymology of the word is somewhat unclear. The traditional example is “a horse’s harness”. Various mathematical as well as non-mathematical meanings of the word are described and analyzed in [188].
- 2.
Fiasko is (of course) Swedish for fiasco. The Hungarian title is more toward “failure” without the disastrous connotation of fiasco.
- 3.
[...] it is not the future that is expecting me, just the next moment, the future does not exist, it is nothing but a perpetual ongoing, a present now. [...] The prediction for my future—is the quality of my present. Translation (from Swedish) and italicization, by the author of this book.
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© 2012 Springer Science+Business Media New York
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Gut, A. (2012). Martingales. In: Probability: A Graduate Course. Springer Texts in Statistics, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4708-5_10
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DOI: https://doi.org/10.1007/978-1-4614-4708-5_10
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