Khantha, M. ; Balakrishnan, V. (1983) First passage time and escape time distributions for continuous time random walks Pramana  Journal of Physics, 21 (3). pp. 187200. ISSN 03044289

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Official URL: http://www.ias.ac.in/j_archive/pramana/21/3/18720...
Related URL: http://dx.doi.org/10.1007/BF02849620
Abstract
We consider an arbitrary continuous time random walk (ctrw)via unbiased nearestneighbour jumps on a linear lattice. Solutions are presented for the distributions of the first passage time and the time of escape from a bounded region. A simple relation between the conditional probability function and the first passage time distribution is analysed. So is the structure of the relation between the characteristic functions of the first passage time and escape time distributions. The mean first passage time is shown to diverge for all (unbiased)ctrw's. The divergence of the mean escape time is related to that of the mean time between jumps. A class ofctrw's displaying a selfsimilar clustering behaviour in time is considered. The exponent characterising the divergence of the mean escape time is shown to be (1H), whereH(0<H<1) is the fractal dimensionality of thectrw.
Item Type:  Article 

Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Continuous Time Random Walk; First Passage Time; Escape Time; Fractal Random Walks 
ID Code:  1056 
Deposited On:  25 Sep 2010 11:08 
Last Modified:  16 May 2016 12:13 
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