Doob martingale (nonfiction): Difference between revisions
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A '''Doob martingale''' (named after Joseph L. Doob, also known as a '''Levy martingale''') is a mathematical construction of a stochastic process which approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approximations to the random variable based on information accumulated up to a certain time. | A '''Doob martingale''' (named after [[Joseph L. Doob (nonfiction)|Joseph L. Doob]], also known as a '''Levy martingale''') is a mathematical construction of a stochastic process which approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approximations to the random variable based on information accumulated up to a certain time. | ||
When analyzing sums, random walks, or other additive functions of independent random variables, one can often apply the central limit theorem, law of large numbers, Chernoff's inequality, Chebyshev's inequality or similar tools. When analyzing similar objects where the differences are not independent, the main tools are martingales and Azuma's inequality. | When analyzing sums, random walks, or other additive functions of independent random variables, one can often apply the central limit theorem, law of large numbers, Chernoff's inequality, Chebyshev's inequality or similar tools. When analyzing similar objects where the differences are not independent, the main tools are martingales and Azuma's inequality. | ||
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== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Joseph L. Doob (nonfiction)]] - Joseph Leo "Joe" Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory. The theory of martingales was developed by Doob. | |||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
Revision as of 08:04, 4 January 2020
A Doob martingale (named after Joseph L. Doob, also known as a Levy martingale) is a mathematical construction of a stochastic process which approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approximations to the random variable based on information accumulated up to a certain time.
When analyzing sums, random walks, or other additive functions of independent random variables, one can often apply the central limit theorem, law of large numbers, Chernoff's inequality, Chebyshev's inequality or similar tools. When analyzing similar objects where the differences are not independent, the main tools are martingales and Azuma's inequality.
In the News
Fiction cross-reference
Nonfiction cross-reference
- Joseph L. Doob (nonfiction) - Joseph Leo "Joe" Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory. The theory of martingales was developed by Doob.
- Mathematics (nonfiction)
External links:
- Doob martingale @ Wikipedia