217 citations · 1.3k across the 28 of their papers we have counts for
23 papers · 1 filter
Semi-fractional diffusion equations
Peter Kern, Svenja Lage, Mark M. Meerschaert
It is well known that certain fractional diffusion equations can be solved by the densities of stable Lévy motions. In this paper we use the classical semigroup approach for Lévy p…
Domain and range symmetries of operator fractional Brownian fields
Gustavo Didier, Mark M. Meerschaert, Vladas Pipiras
An operator fractional Brownian field (OFBF) is a Gaussian, stationary increment R^n-valued random field on R^m that satisfies the operator self-similarity property {X(c^E t)}_{t i…
Exponents of operator self-similar random fields
Gustavo Didier, Mark M. Meerschaert, Vladas Pipiras
If X(c^E t) and c^H X(t) have the same finite-dimensional distributions for some linear operators E and H, we say that the random vector field X(t) is operator self-similar. The ex…
Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties
Peter Kern, Mark M. Meerschaert, Yimin Xiao
This paper proves sharp bounds on the tails of the Lévy exponent of an operator semistable law on . These bounds are then applied to explicitly compute the Hausdorff a…
Space-time fractional Dirichlet problems
Boris Baeumer, Tomasz Luks, Mark M. Meerschaert
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an…
Relaxation patterns and semi-Markov dynamics
Mark M. Meerschaert, Bruno Toaldo
Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variet…
Reflected Spectrally Negative Stable Processes and their Governing Equations
Boris Baeumer, Mihály Kovács, Mark M. Meerschaert +2
This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward e…
Correction: Limit theorems for coupled continuous time random walks
Peter Kern, Mark M. Meerschaert, Hans-Peter Scheffler
Correction to "Limit theorems for coupled continuous time random walks" (Ann. Probab. 32 (2004) 730-756).
Semi-Markov approach to continuous time random walk limit processes
Mark M. Meerschaert, Peter Straka
Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limit…
Space-time fractional diffusion on bounded domains
Zhen-Qing Chen, Mark M. Meerschaert, Erkan Nane
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. T…
Fractal Dimensions for Continuous Time Random Walk Limits
Mark M. Meerschaert, Erkan Nane, Yimin Xiao
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer pr…
The fractional Poisson process and the inverse stable subordinator
Mark M. Meerschaert, Erkan Nane, P. Vellaisamy
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a P…
Tempered stable laws as random walk limits
Arijit Chakrabarty, Mark M. Meerschaert
Stable laws can be tempered by modifying the Lévy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and in…
Transient anomalous sub-diffusion on bounded domains
Erkan Nane, Mark M. Meerschaert, Palaniappan Vellaisamy
This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractiona…
Modeling and simulation with operator scaling
Serge Cohen, Mark M. Meerschaert, Jan Rosinski
Self-similar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper dev…
Distributed-order fractional Cauchy problems on bounded domains
Mark M. Meerschaert, Erkan Nane, Palaniappan Vellaisamy
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. T…
Space-time duality for fractional diffusion
Boris Baeumer, Mark M. Meerschaert, Erkan Nane
Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional…
Local times of multifractional Brownian sheets
Mark Meerschaert, Dongsheng Wu, Yimin Xiao
Denote by a function in with values in . Let be an -multifr…
Correlated continuous time random walks
Mark M. Meerschaert, Erkan Nane, Yimin Xiao
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolutio…
Fractional Cauchy problems on bounded domains
Mark M. Meerschaert, Erkan Nane, P. Vellaisamy
Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional…
Large deviations for local time fractional Brownian motion and applications
Mark M. Meerschaert, Erkan Nane, Yimin Xiao
Let $W^H=\{W^H(t), t \in \rr\}$ be a fractional Brownian motion of Hurst index with values in $\rr$, and let be the local time process at zero…
Brownian subordinators and fractional Cauchy problems
Boris Baeumer, Mark M. Meerschaert, Erkan Nane
A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value pr…
Operator Scaling Stable Random Fields
Hermine Biermé, Mark M. Meerschaert, Hans-Peter Scheffler
A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a movin…