Abstract
We consider a random walk with drift to the left. LetM n denote the extreme position to the right of the particle during its firstn steps. An approximate expression for the characteristic function of the distribution of this random variable is evaluated. The numerical inversion of this characteristic function is performed with the aid of the Fast Fourier Transform.
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References
W. Feller,An introduction to probability theory and its applications, vol. II. New York, Wiley 1966.
H. Bohman,To compute the distribution function when the characteristic function is known, Skand. Aktuar. Tidskr. 1963.
J. W. Cooley, P. A. W. Lewis, and P. D. Welch,The Fast Fourier Transform and its application, IEEE Transactions on Education, vol. E-12, No. 1, 27–34 (1969).
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Bohman, H. On the maximum deviation in random walks. BIT 11, 133–138 (1971). https://doi.org/10.1007/BF01934361
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DOI: https://doi.org/10.1007/BF01934361