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

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

2008-12-11

arxiv.org/abs/0812.2148v1

Chaos, Solitons and Fractals 42, 128-137 (2009)

Economy

Quantitative Finance

Statistical Finance

elsart, 12 pages, 3 figures, accepted for publication in Chaos, Solitons & Fractals

Scientific paper

10.1016/j.chaos.2008.11.015

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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