151 citations · 336 across the 14 of their papers we have counts for
14 papers
A Universal Algorithm for Continuous Time Random Walks Limit Distributions
Gurtek Gill, Peter Straka
In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Alt…
Statistical Inference for inter-arrival times of extreme events in bursty time series
Katharina Hees, Smarak Nayak, Peter Straka
In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The…
Variable Order Fractional Fokker-Planck Equations derived from Continuous Time Random Walks
Peter Straka
Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent varies in space. This type of situation occurs e.g. in b…
A Semi-Markov Algorithm for Continuous Time Random Walk Limit Distributions
G. Gill, P. Straka
The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their limit processes is utilized, and the probability distributions of the bivariate Markov process $(X(t),V(t…
Fractal Curvature Measures and Image Analysis
Peter Straka
Since the recent dissertation by Steffen Winter, for certain self-similar sets the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \…
Fokker--Planck and Kolmogorov Backward Equations for Continuous Time Random Walk scaling limits
Boris Baeumer, Peter Straka
It is proved that the distributions of scaling limits of Continuous Time Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck Equations for diffusion pro…
Estimation of fractal dimension and fractal curvatures from digital images
Evgeny Spodarev, Peter Straka, Steffen Winter
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel set…
Limit Theorems and Governing Equations for Levy Walks
M. Magdziarz, H. P. Scheffler, P. Straka +1
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the…
Transport Equations for Subdiffusion with Nonlinear Particle Interaction
Peter Straka, Sergei Fedotov
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To t…
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…
Forward and Backward Governing EQuations for Anomalous Diffusion Models Based on the Continuous Time Random Walk
Peter Straka
Continuous Time Random Walks (CTRWs) are jump processes with random waiting times between jumps. We study scaling limits for CTRWs where the distribution of jumps and waiting times…
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…
Lagging/Leading Coupled Continuous Time Random Walks, Renewal Times and their Joint Limits
Peter Straka, Bruce Ian Henry
Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW) model for diffusion, including the possibility of anomalous diffusion. Transition densi…
Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
B. I. Henry, T. A. M Langlands, P. Straka
We have derived a fractional Fokker-Planck equation for subdiffusion in a general space-and- time-dependent force field from power law waiting time continuous time random walks bia…