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Continuity Properties of Distributions with Some Decomposability

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  • Toshiro Watanabe

Abstract

Absolute continuity and smoothness of distributions in the nested subclasses ~L m(B), m = 0, 1, 2,..., of the class of all B-decomposable distributions are studied. All invertible matrices are classified into two types in terms of P.V. numbers. The minimum integer m for which all full distributions in ~L m(B) are absolutely continuous and the minimum integer m for which all absolutely continuous distributions in ~L m(B) have the densities of class C r for 0 ≤ r ≤ ∞ are discussed according to the type of the matrix B related to P.V. numbers.

Suggested Citation

  • Toshiro Watanabe, 2000. "Continuity Properties of Distributions with Some Decomposability," Journal of Theoretical Probability, Springer, vol. 13(1), pages 169-191, January.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:1:d:10.1023_a:1007739010953
    DOI: 10.1023/A:1007739010953
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    References listed on IDEAS

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    1. Sato, Ken-iti, 1982. "Absolute continuity of multivariate distributions of class L," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 89-94, March.
    2. Yamazato, Makoto, 1983. "Absolute continuity of operator-self-decomposable distributions on Rd," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 550-560, December.
    3. Wolfe, Stephen James, 1983. "Continuity properties of decomposable probability measures on euclidean spaces," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 534-538, December.
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    Cited by:

    1. Toshiro Watanabe, 2002. "Shift Self-Similar Additive Random Sequences Associated with Supercritical Branching Processes," Journal of Theoretical Probability, Springer, vol. 15(3), pages 631-665, July.
    2. Toshiro Watanabe, 2016. "Escape Rates for Multidimensional Shift Self-similar Additive Sequences," Journal of Theoretical Probability, Springer, vol. 29(3), pages 896-921, September.

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