Abstract
Let the distribution of\(\ell n\) X be that of the first passage times of standard Brownian motion. Properties of the distribution ofX are considered, and results concerning the maximum likelihood estimate ofE (1/X) are described.
Similar content being viewed by others
References
AITCHISON, J. and BROWN, J.A.C.: “The Lognormal Distribution”, Cambridge University Press, 1963.
ITÔ, KUJOSI and McKEAN, Henry P. Jr.: “Diffusion Processes and Their Sample Paths”, Springer-Verlag, Berlin, 1965.
KULDORFF, Gunnar.: “Contributions to the Theory of Estimation From Grouped and Partially Grouped Samples”, Almquist and Wiksell, Uppsala, Sweden, 1961.
LÉVY, PAUL.: “Sur Certain Processus Stochastiques Homogenes”, Compositio Mathematica 7 (40), pp. 283–339.
ROY, L.K. and WASAN, M.T.: “Some Characteristic Properties of the Time Distribution of Standard Brownian Motion”, Publication de l’Institut de Statistique de l’Université de Paris, 17(68) Fasc. 3.
ROY, L.K. and WASAN, M.T.: “Properties of the Time Distribution of Standard Brownian Motion”, Trabajos de Estadística 19(68) pp. 67–82.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roy, L.K. The logarithmic distribution of first passage times of standard Brownian motion. Trab. Estad. Invest. Oper. 23, 125–128 (1972). https://doi.org/10.1007/BF03004953
Issue Date:
DOI: https://doi.org/10.1007/BF03004953