Geodesic
Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 684-703

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Functional limit theorems for continuous-time random walks (CTRW) are found in the general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes.
Mots-clés : fractional stable distributions, anomalous diffusion
Keywords: fractional derivatives, limit theorems, continuous-time random walks, time change, Lйvy subordinators, hitting time processes. 
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     author = {V. N. Kolokoltsov},
     title = {Generalized {Continuous-Time} {Random} {Walks,} {Subordination} by {Hitting} {Times,} and {Fractional} {Dynamics}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a2/}
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V. N. Kolokoltsov. Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 684-703. http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a2/