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Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 4, Pages 684–703 (Mi tvp2460)  

This article is cited in 32 scientific papers (total in 32 papers)

Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics

V. N. Kolokoltsov

Nottingham Trent University

Abstract: 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.

Keywords: fractional stable distributions, anomalous diffusion, fractional derivatives, limit theorems, continuous-time random walks, time change, Lйvy subordinators, hitting time processes.

DOI: https://doi.org/10.4213/tvp2460

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English version:
Theory of Probability and its Applications, 2009, 53:4, 594–609

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Received: 30.11.2007

Citation: V. N. Kolokoltsov, “Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics”, Teor. Veroyatnost. i Primenen., 53:4 (2008), 684–703; Theory Probab. Appl., 53:4 (2009), 594–609

Citation in format AMSBIB
\by V.~N.~Kolokoltsov
\paper Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 4
\pages 684--703
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 4
\pages 594--609

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    2. Hahn M.G., Kobayashi K., Umarov S., “Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion”, Proc. Amer. Math. Soc., 139:2 (2011), 691–705  crossref  mathscinet  zmath  isi  elib  scopus
    3. Hahn M., Umarov S., “Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations”, Fract. Calc. Appl. Anal., 14:1 (2011), 56–79  crossref  mathscinet  zmath  isi  elib  scopus
    4. Jara M., Komorowski T., “Limit theorems for some continuous-time random walks”, Adv. in Appl. Probab., 43:3 (2011), 782–813  crossref  mathscinet  zmath  isi  scopus
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