Tempered stable Lévy motion and transient super-diffusion
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Publication:847223
DOI10.1016/j.cam.2009.10.027zbMath1423.60079OpenAlexW2065697505MaRDI QIDQ847223
Mark M. Meerschaert, Boris Baeumer
Publication date: 12 February 2010
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2009.10.027
Processes with independent increments; Lévy processes (60G51) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) PDEs with randomness, stochastic partial differential equations (35R60) Fractional partial differential equations (35R11)
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Cites Work
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- Unnamed Item
- Aspects of de La Vallée Poussin's work in approximation and its influence
- An algorithm for evaluating stable densities in Zolotarev's \((M)\) parameterization
- Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes
- Tempering stable processes
- Finite difference approximations for fractional advection-dispersion flow equations
- Lévy flights and related topics in physics. Proceedings of the international workshop, held at Nice, France, 27-30 June, 1994
- A second-order accurate numerical approximation for the fractional diffusion equation
- On using random walks to solve the space-fractional advection-dispersion equations
- Discretized Fractional Calculus
- A Method for Simulating Stable Random Variables
- Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight
- Limit theorems for continuous-time random walks with infinite mean waiting times
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
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