Rates of convergence in the functional CLT for multidimensional continuous time martingales. (Q1879506)
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scientific article; zbMATH DE number 2102361
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| English | Rates of convergence in the functional CLT for multidimensional continuous time martingales. |
scientific article; zbMATH DE number 2102361 |
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Rates of convergence in the functional CLT for multidimensional continuous time martingales. (English)
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22 September 2004
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A speed of convergence in the multidimensional functional CLT for martingales can be measured by means of the Prokhorov's distance between a Brownian motion and the martingale. Assuming square integrability the paper presents an estimation of that distance. The estimate contains uniform Ky Fan's distance between quadratic variation of the considered martingale and the variance of Brownian bridge, and the influence of jumps measured by their uniform Ky Fan's distance from zero process, only. The last section of the paper compares the reached result with known results.
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multidimensional martingale
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multidimensional Brownian motion
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Prokhorov's distance
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Ky Fan's distance
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uniform Ky Fan's distance
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quadratic covariation of two square integrable martingales
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quadratic variation of a square integrable martingale
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