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2 results

  • INEQUALITIES AND UNIFORM ASYMPTOTIC FORMULAE FOR SPT-CRANK OF PARTITIONS

  • Part of
  • YUAN CHEN, NIAN HONG ZHOU
  • Journal:
    Bulletin of the Australian Mathematical Society , First View
    Published online by Cambridge University Press:
    13 September 2024, pp. 1-12
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  • We establish some inequalities that arise from truncating Lerch sums and derive uniform asymptotic formulae for the spt-crank of ordinary partitions. The uniform asymptotic formulae improve upon a result of Mao [‘Asymptotic formulas for spt-crank of partitions’, J. Math. Anal. Appl. 460(1) (2018), 121–139].

  • The finite-time ruin probability of the compound Poisson model with constant interest force

  • Part of
  • Qihe Tang
  • Journal:
    Journal of Applied Probability / Volume 42 / Issue 3 / September 2005
    Published online by Cambridge University Press:
    14 July 2016, pp. 608-619
    Print publication:
    September 2005
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  • In this paper, we establish a simple asymptotic formula for the finite-time ruin probability of the compound Poisson model with constant interest force and subexponential claims in the case that the initial surplus is large. The formula is consistent with known results for the ultimate ruin probability and, in particular, is uniform for all time horizons when the claim size distribution is regularly varying tailed.