151 citations · 336 across the 14 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…