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The influence of a power law drift on the exit time of Brownian motion from a half-line

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  • DeBlassie, Dante
  • Smits, Robert

Abstract

The addition of a Bessel drift to a Brownian motion affects the lifetime of the process in the interval (0,[infinity]) in a well-understood way. We study the corresponding effect of a power of the Bessel drift. The most interesting case occurs when [beta]>0. If p>1 then the effect of the drift is not too great in the sense that the exit time has the same critical value q0 for the existence of qth moments (q>0) as the exit time of Brownian motion. When p

Suggested Citation

  • DeBlassie, Dante & Smits, Robert, 2007. "The influence of a power law drift on the exit time of Brownian motion from a half-line," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 629-654, May.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:5:p:629-654
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    1. Cox, John C. & Ingersoll Junior, Jonathan E. & Ross, Stephen A., 2007. "A theory of the term structure of interest rates," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 47(2), April.
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    1. Menshikov, Mikhail V. & Wade, Andrew R., 2010. "Rate of escape and central limit theorem for the supercritical Lamperti problem," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2078-2099, September.

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