First passage time distributions for finite one-dimensional random walks |
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Authors: | M Khantha V Balakrishnan |
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Institution: | (1) Department of Physics, Indian Institute of Technology, 600 036 Madras, India |
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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 Lévy distribution with exponent 1/2 as the boundary tends to ∞. |
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Keywords: | Biased random walks Markov processes first passage time finite chains |
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