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Negative Definite Kernels and Metrics: Recovering Measures from Potentials

In: The Methods of Distances in the Theory of Probability and Statistics

Author

Listed:
  • Svetlozar T. Rachev

    (Stony Brook University, Department of Applied Mathematics and Statistics College of Business
    FinAnalytica)

  • Lev B. Klebanov

    (Charles University, Department of Probability and Statistics)

  • Stoyan V. Stoyanov

    (EDHEC Business School EDHEC-Risk Institute)

  • Frank J. Fabozzi

    (EDHEC Business School EDHEC-Risk Institute)

Abstract

Introduce probability metrics through strongly negative definite kernel functions and provide examples, Introduce probability metrics through m-negative definite kernels and provide examples, Introduce the notion of potential corresponding to a probability measure, Present the problem of recovering a probability measure from its potential, Consider the relation between the problems of convergence of measures and the convergence of their potentials, Characterize probability distributions using the theory of recovering probability measures from potentials.

Suggested Citation

  • Svetlozar T. Rachev & Lev B. Klebanov & Stoyan V. Stoyanov & Frank J. Fabozzi, 2013. "Negative Definite Kernels and Metrics: Recovering Measures from Potentials," Springer Books, in: The Methods of Distances in the Theory of Probability and Statistics, edition 127, chapter 0, pages 539-569, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-4869-3_22
    DOI: 10.1007/978-1-4614-4869-3_22
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