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2 results

  • A NOTE ON THE CLOSURE OF CONVOLUTION POWER MIXTURES (RANDOM SUMS) OF EXPONENTIAL DISTRIBUTIONS

  • Part of
  • J. M. P. ALBIN
  • Journal:
    Journal of the Australian Mathematical Society / Volume 84 / Issue 1 / February 2008
    Published online by Cambridge University Press:
    01 February 2008, pp. 1-7
    Print publication:
    February 2008
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  • We make a correction to an important result by Cline [D. B. H. Cline, ‘Convolutions of distributions with exponential tails’, J. Austral. Math. Soc. (Series A)43 (1987), 347–365; D. B. H. Cline, ‘Convolutions of distributions with exponential tails: corrigendum’, J. Austral. Math. Soc. (Series A)48 (1990), 152–153] on the closure of the exponential class under convolution power mixtures (random summation).

  • A Lower Estimate for Central Probabilities on Polycyclic Groups

  • G. Alexopoulos
  • Journal:
    Canadian Journal of Mathematics / Volume 44 / Issue 5 / 01 October 1992
    Published online by Cambridge University Press:
    20 November 2018, pp. 897-910
    Print publication:
    01 October 1992
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  • We give a lower estimate for the central value μ*n(e) of the nth convolution power μ*···*μ of a symmetric probability measure μ on a polycyclic group G of exponential growth whose support is finite and generates G. We also give a similar large time diagonal estimate for the fundamendal solution of the equation (∂/∂t + L)u = 0, where L is a left invariant sub-Laplacian on a unimodular amenable Lie group G of exponential growth.