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Main directions in the theory of probability metrics |
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Probability distances and probability metrics: Definitions |
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Primary, simple and compound probability distances, and minimal and maximal distances and norms |
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A structural classification of probability distances.-Monge-Kantorovich mass transference problem, minimal distances and minimal norms |
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Quantitative relationships between minimal distances and minimal norms |
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K-Minimal metrics |
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Relations between minimal and maximal distances |
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Moment problems related to the theory of probability metrics: Relations between compound and primary distances |
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Moment distances |
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Uniformity in weak and vague convergence |
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Glivenko-Cantelli theorem and Bernstein-Kantorovich invariance principle |
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Stability of queueing systems.-Optimal quality usage |
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Ideal metrics with respect to summation scheme for i.i.d. random variables |
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Ideal metrics and rate of convergence in the CLT for random motions |
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Applications of ideal metrics for sums of i.i.d. random variables to the problems of stability and approximation in risk theory |
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How close are the individual and collective models in risk theory?- Ideal metric with respect to maxima scheme of i.i.d. random elements |
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Ideal metrics and stability of characterizations of probability distributions |
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Positive and negative de nite kernels and their properties |
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Negative definite kernels and metrics: Recovering measures from potential |
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Statistical estimates obtained by the minimal distances method |
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Some statistical tests based on N-distances |
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Distances defined by zonoids |
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N-distance tests of uniformity on the hypersphere.- |
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Main directions in the theory of probability metrics |
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Probability distances and probability metrics: Definitions |
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Primary, simple and compound probability distances, and minimal and maximal distances and norms |
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