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On properties of Continuous-Time Random Walks with Non-Poissonian jump-times

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  • Javier Villarroel
  • Miquel Montero

Abstract

The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The case of Erlang distributed times is analyzed in detail. Several concrete examples are considered.

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File URL: http://arxiv.org/pdf/0812.2148
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Paper provided by arXiv.org in its series Papers with number 0812.2148.

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Date of creation: Dec 2008
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Publication status: Published in Chaos, Solitons and Fractals 42, 128-137 (2009)
Handle: RePEc:arx:papers:0812.2148

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  1. Jaume Masoliver & Miquel Montero & George H. Weiss, 2002. "A continuous time random walk model for financial distributions," Papers cond-mat/0210513, arXiv.org.
  2. R. Kutner & F. SwitaƂa, 2003. "Stochastic simulations of time series within Weierstrass-Mandelbrot walks," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 201-211.
  3. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
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