Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (5): 1206-1212.

• Articles • Previous Articles     Next Articles

Asymptotics for the Density of the Supremum of a Certain Kind of Random Walks

  

  1. School of Mathematical Science, Soochow University, Jiangsu Suzhou 215006
  • Received:2007-05-25 Revised:2008-09-30 Online:2009-10-25 Published:2009-10-25
  • Supported by:

    国家自然科学基金(10671193)、江苏省高校自然科学基础研究项目(08KJD110005)和数学天元青年基金(10826043)资助

Abstract:

Kluppelberg[1], Asmussen et al. [2] obtained asymptotics for the density of the supremum of a random walk with a finite negative mean. While this paper further investigates the case of a random walk with negative infinite mean on the basis of Denisov et al. [3] and Wang and Cheng[4]. To illustrate that some common distributions satisfy the conditions of the obtained results,  the authors discuss some properties of certain density classes.

Key words: The supremum of a random walk, Negative infinite mean, Class of subexponential densities, Asymptotics

CLC Number: 

  • 60G50
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