Abstract
We studythe distribution of first passage time for Levyt ype anomalous diffusion. A fractional Fokker-Planck equation framework is introduced. For the zero drift case, using fractional calculus an explicit analytic solution for the first passage time densityfunction in terms of Fox or H-functions is given. The asymptotic behaviour of the densityfunction is discussed. For the nonzero drift case, we obtain an expression for the Laplace transform of the first passage time densityfunction, from which the mean first passage time and variance are derived.
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Rangarajan, G., Ding, M. (2003). First Passage Distributions for Long Memory Processes. In: Rangarajan, G., Ding, M. (eds) Processes with Long-Range Correlations. Lecture Notes in Physics, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44832-2_9
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DOI: https://doi.org/10.1007/3-540-44832-2_9
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