Limit theorems for continuous-time random walks with infinite mean waiting times

By Mark M. Meerschaert, Hans-Peter Scheffler. Journal of Applied Probability, 2004

512 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a80639c34fff7600c345620efafabf5516c8ed4d

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Citations in the corpus

Fractional conservation of mass (2008, background): “The fractional advection dispersion equation is known to be a special case of a general transport equation with convolution flux [7] and a limit case of the continuous time random walk with power-law particle jumps [4,10].”
Distributed-order fractional diffusions on bounded domains (2009, background): “The process B(Et) is the long-time scaling limit of a random walk [24,25], when the random waiting times between jumps belong to the β-stable domain of attraction.”
Numerical Computation of First-Passage Times of Increasing Lévy Processes (2009, background): “Inverse subordinators are of particular interest in the study of fractional kinetics and the scaling limits of continuous time random walks, [7], [8], [20], [24], [4].”
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, unknown): “…the special case µ = 1/2 reveals the FPTD a(πx0)−1/2 exp(−a2t2/(4x0)) where a is the amplitude of the Lévy stable law, and x0 is the distance of the absorbing barrier from the initial location (Eliazar and Klafter 2004); compare also to the detailed discussion in Meerschaert and Scheffler 2004.”
Convolution-Type Derivatives, Hitting-Times of Subordinators and Time-Changed C0-semigroups (2013, background): “The logic of our definitions starts from the observation of the fractional derivative of order α ∈ (0, 1) (in the Riemann-Liouville sense) can be considered the first-order derivative of the Laplace convolution u(t) ∗ t−α/Γ(1−α) (see Kilbas et al. [15]) dα dtα u(t) = 1 Γ(1− α) d dt ∫ t 0 u(s) (t− s)”
The Fractional Poisson Process and the Inverse Stable Subordinator (2010, unknown): “1 in [34]), so that P (Jn > t) = E[exp(−λE(t))].”
Space-time fractional diffusion on bounded domains (2011, unknown): “1) For more details, see [3,8].”
A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations (2009, unknown): “See [21,22] for more details.”
Fractional advection‐dispersion equations for modeling transport at the Earth surface (2009, background): “If g(t) is the pdf of W, a change of variables [ Meerschaert and Scheffler,2004 ] shows thatu= (t/W)g has pdf”
Aging renewal theory and application to random walks (2013, unknown): “[13,16,34,35] and references therein.”
Parameter estimation for fractional transport: A particle‐tracking approach (2009, methodology): “The validity of this procedure for the CTRW model is supported by Meerschaert and Scheffler [2004] where the CTRW ergodic limit is proven to be a time-fractional ADE.”