Triangular array limits for continuous time random walks

By Mark M. Meerschaert, Hans-Peter Scheffler. 2008

219 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/63cfd3913460dfc2db1dd824b1b753fab8b3e021

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Citations in the corpus

Stochastic Calculus for a Time-Changed Semimartingale and the Associated Stochastic Differential Equations (2009, background): “The new feature is the coexistence of a usual drift term along with a term related to the time-change.”
General Fractional Calculus, Evolution Equations, and Renewal Processes (2011, background): “5) (and more general problems, with Lévy generators instead of the Laplacian) was found in [22, 23].”
A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations (2009, background): “Because TðuÞ is an infinitely divisible process whose density lðt;uÞ has LT e uLðsÞ, a general theory [22] shows that the process”
Tempered anomalous diffusion in heterogeneous systems (2008, background): “An efficient particle tracking solution for equation (4) tracks x = A(u) at operational time u = E(t) via the equivalent relation t = D(u), since the Markov process D(u) is easier to simulate than its non-Markovian inverse [ Meerschaert and Scheffler, 2008 ].”
Time fractional equations and probabilistic representation (2017, background): “(ii) There are two closely related work [19, 12].”
SDEs Driven by a Time-Changed Lévy Process and Their Associated Time-Fractional Order Pseudo-Differential Equations (2009, unknown): “: 1-617-627-2363 Fax: 1-617-627-3966 E-mail: marjorie.hahn@tufts.edu K. Kobayashi Department of Mathematics, Tufts University, Medford, MA 02155 E-mail: kei.kobayashi@tufts.edu S.Umarov Department of Mathematics, Tufts University, Medford, MA 02155 E-mail: sabir.umarov@tufts.edu 2”
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)”
Asymptotic properties of Brownian motion delayed by inverse subordinators (2013, background): “It is straightforward to verify that where s ( x, t ) is the probability density function of f S ( t ) (existence of s ( y, t ) under the assumption ν (0 , ∞ ) = ∞ was proved in [41] Theorem 3.1).”
The Fractional Poisson Process and the Inverse Stable Subordinator (2010, background): “A general theory of CTRW scaling limits and governing equations is developed in [36].”
Inverse Tempered Stable Subordinators (2014, background): “For a strictly increasing subordinator Y (t) with density function p(x, t) and Laplace symbol ΨY (s), the density function q(x, t) of the hitting time process has the LT (e.g., see Meerschaert and Scheffler (2008a)) Lt(q(x, t)) = 1 s ΨY (s)e −xΨY (s).”
Distributed-order fractional diffusions on bounded domains (2009, background): “1 in [27] implies that Et has a Lebesgue density g(t, x) = t ∫”
Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, background): “The CTRW Xt 1⁄4 SNt has the scaling limit process AðUðtÞÞ, which is a subordination that replaces the time parameter t in the scaling limit jump process AðtÞ by the hitting time process UðtÞ [98].”