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Asymptotic property of the distribution of the maxima of a random walk

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  • Alam, Khursheed

Abstract

Let F be a univariate distribution with negative expectation, and let M denote the distribution of the positive maxima of a random walk generated by a sequence of independent observations from F. We consider the Laplace transforms of 1-F(x) and 1-M(x). A relation between the transforms yields some known results on the moments and the regularly varying properties of the two distributions.

Suggested Citation

  • Alam, Khursheed, 1978. "Asymptotic property of the distribution of the maxima of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 7(3), pages 337-340, August.
    • Handle: RePEc:eee:spapps:v:7:y:1978:i:3:p:337-340
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