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Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice
Preface. Acknowledgments. INTRODUCTION. Random Vectors. Linear Operators. Infinitely Divisible Distributions and Triangular Arrays. MULTIVARIATE REGULAR VARIATION. Regular Variations for Linear…
Limit theorems for continuous-time random walks with infinite mean waiting times
A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has…
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A second-order accurate numerical approximation for the fractional diffusion equation
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Operator scaling stable random fields
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Finite difference methods for two-dimensional fractional dispersion equation
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Triangular array limits for continuous time random walks
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Limit theorems for coupled continuous time random walks
Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion.…
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Stochastic solution of space-time fractional diffusion equations.
TLDR
Replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type, leading to explicit solutions for space-time fractional diffusion equations with multiscaling space-fractional derivatives.
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Fractional governing equations for coupled random walks
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Stochastic model for ultraslow diffusion
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