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Continuity properties of decomposable probability measures on euclidean spaces

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  • Wolfe, Stephen James

Abstract

It is shown that every full eA decomposable probability measure on Rk, where A is a linear operator all of whose eigenvalues have negative real part, is either absolutely continuous with respect to Lebesgue measure or continuous singular with respect to Lebesgue measure. This result is used to characterize the continuity properties of random variables that are limits of solutions of certain stochastic difference equations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:4:p:534-538
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    Cited by:

    1. Becker-Kern, Peter & Pap, Gyula, 2008. "Parameter estimation of selfsimilarity exponents," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 117-140, January.
    2. Toshiro Watanabe, 2000. "Continuity Properties of Distributions with Some Decomposability," Journal of Theoretical Probability, Springer, vol. 13(1), pages 169-191, January.
    3. 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.

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