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Regular Variation in R k
Researchers investigating certain limit theorems in probability have discovered a multivariable analogue to Karamata's theory of regularly varying functions. The method uses elements of real analysis…
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Finite difference approximations for fractional advection-dispersion flow equations
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Finite difference approximations for two-sided space-fractional partial differential equations
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Stochastic Models for Fractional Calculus
Preface: 1 Introduction 1.1 The traditional diffusion model 1.2 Fractional diffusion 2 Fractional Derivatives 2.1 The Grunwald formula 2.2 More fractional derivatives 2.3 The Caputo derivative 2.4…
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Application of a fractional advection‐dispersion equation
A transport equation that uses fractional‐order dispersion derivatives has fundamental solutions that are Lévy's α‐stable densities. These densities represent plumes that spread proportional to time…
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Parameter Estimation for the Truncated Pareto Distribution
The Pareto distribution is a simple model for nonnegative data with a power law probability tail. In many practical applications, there is a natural upper bound that truncates the probability tail.…
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The fractional‐order governing equation of Lévy Motion
A governing equation of stable random walks is developed in one dimension. This Fokker‐Planck equation is similar to, and contains as a subset, the second‐order advection dispersion equation (ADE)…
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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…
Fractal mobile/immobile solute transport
A fractal mobile/immobile model for solute transport assumes power law waiting times in the immobile zone, leading to a fractional time derivative in the model equations. The equations are equivalent…
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STOCHASTIC SOLUTIONS FOR FRACTIONAL CAUCHY PROBLEMS
Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional…
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