First passage time distributions for finite one-dimensional random walks

Khantha, M. ; Balakrishnan, V. (1983) First passage time distributions for finite one-dimensional random walks Pramana - Journal of Physics, 21 (2). pp. 111-122. ISSN 0304-4289

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Official URL: http://www.ias.ac.in/j_archive/pramana/21/2/111-12...

Related URL: http://dx.doi.org/10.1007/BF02894735

Abstract

We present closed expressions for the characteristic function of the first passage time distribution for biased and unbiased random walks on finite chains and continuous segments with reflecting boundary conditions. Earlier results on mean first passage times for one-dimensional random walks emerge as special cases. The divergences that result as the boundary is moved out to infinity are exhibited explicitly. For a symmetric random walk on a line, the distribution is an elliptic theta function that goes over into the known Levy distribution with exponent ½ as the boundary tends to infinity.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Biased Random Walks; Markov Processes; First Passage Time; Finite Chains
ID Code:1073
Deposited On:25 Sep 2010 11:24
Last Modified:16 May 2016 12:14

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