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2 results

  • Explicit bounds for third-order difference equations

  • Kenneth S. Berenhaut, Eva G. Goedhart, Stevo Stević
  • Journal:
    The ANZIAM Journal / Volume 47 / Issue 3 / January 2006
    Published online by Cambridge University Press:
    17 February 2009, pp. 359-366
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  • This paper gives explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher-order equations. The results extend recent work of the authors for second-order equations.

  • On explicit and Fréchet-optimal lower bounds

  • Part of
  • Eugene Seneta, John Tuhao Chen
  • Journal:
    Journal of Applied Probability / Volume 39 / Issue 1 / March 2002
    Published online by Cambridge University Press:
    14 July 2016, pp. 81-90
    Print publication:
    March 2002

  • Ease of computation of Fréchet-optimal lower bounds, given numerical values of the binomial moments Sij, i, j = 1, 2, is demonstrated. A sufficient condition is given for an explicit bivariate bound of Dawson-Sankoff structure to be Fréchet optimal. An example demonstrates that in the bivariate case even the multiplicative structure of the Sij does not guarantee a Dawson-Sankoff structure for Fréchet-optimal bounds. A final section is used to illuminate the nature of Fréchet optimality by using generalized explicit bounds. This note is a sequel to both Chen and Seneta (1995) and Chen (1998).