Triangular array limits for continuous time random walks
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Publication:947153
DOI10.1016/j.spa.2007.10.005zbMath1153.60023OpenAlexW2044729651MaRDI QIDQ947153
Mark M. Meerschaert, Hans-Peter Scheffler
Publication date: 29 September 2008
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.spa.2007.10.005
Sums of independent random variables; random walks (60G50) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Functional limit theorems; invariance principles (60F17)
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Cites Work
- Unnamed Item
- Unnamed Item
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- Unnamed Item
- Unnamed Item
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- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fractional kinetic equation for Hamiltonian chaos
- High risk scenarios and extremes. A geometric approach
- Semigroups of linear operators and applications to partial differential equations
- Random walks with infinite spatial and temporal moments
- One-parameter semigroups of positive operators
- Waiting-times and returns in high-frequency financial data: An empirical study
- Limit theorems for coupled continuous time random walks.
- Infinite divisibility of random variables and their integer parts
- A fractional diffusion equation to describe Lévy flights
- Stochastic model for ultraslow diffusion
- Stochastic-Process Limits
- Ultrafast subordinators and their hitting times
- On Subordinated Holomorphic Semigroups
- 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
- Space-time fractional derivative operators
- Limit theorem for continuous-time random walks with two time scales
- Fractional kinetic equations: solutions and applications
- Chance and Stability
- Limit theorems for occupation times of Markov processes
- A convolution equation and hitting probabilities of single points for processes with stationary independent increments
- The random walk's guide to anomalous diffusion: A fractional dynamics approach