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Regular Variation in R k

- M. Meerschaert
- Mathematics
- 1 February 1988

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… Expand

Finite difference approximations for fractional advection-dispersion flow equations

- M. Meerschaert, C. Tadjeran
- Mathematics, Environmental Science
- 1 November 2004

Finite difference approximations for two-sided space-fractional partial differential equations

- M. Meerschaert, C. Tadjeran
- Mathematics
- 2006

Stochastic Models for Fractional Calculus

- M. Meerschaert, A. Sikorskii
- Mathematics
- 23 December 2011

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… Expand

Application of a fractional advection‐dispersion equation

- D. Benson, S. Wheatcraft, M. Meerschaert
- Mathematics
- 1 February 2000

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… Expand

Parameter Estimation for the Truncated Pareto Distribution

- I. Aban, M. Meerschaert, A. Panorska
- Mathematics
- 1 March 2006

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.… Expand

The fractional‐order governing equation of Lévy Motion

- D. Benson, S. Wheatcraft, M. Meerschaert
- Mathematics
- 1 February 2000

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)… Expand

Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice

- H. Scheffler, M. Meerschaert
- Mathematics
- 11 July 2001

Preface. Acknowledgments. INTRODUCTION. Random Vectors. Linear Operators. Infinitely Divisible Distributions and Triangular Arrays. MULTIVARIATE REGULAR VARIATION. Regular Variations for Linear… Expand

Fractal mobile/immobile solute transport

- R. Schumer, D. Benson, M. Meerschaert, B. Baeumer
- Physics
- 1 October 2003

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… Expand

STOCHASTIC SOLUTIONS FOR FRACTIONAL CAUCHY PROBLEMS

- B. Baeumer, M. Meerschaert
- Mathematics
- 2003

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… Expand

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