scholarly journals Continuous time random walk and diffusion with generalized fractional Poisson process

2020 ◽  
Vol 545 ◽  
pp. 123294 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Alejandro P. Riascos
Keyword(s):  
Random Walk ◽  
Poisson Process ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Fractional Poisson Process ◽  
And Diffusion

scholarly journals Continuous time random walk model with advection and diffusion as two distinct dynamical origins

2019 ◽  
Vol 68 (13) ◽  
pp. 130501
Author(s):  
Xiao-Rong Yang ◽  
Qiong Wang ◽  
Tang-Jin Ye ◽  
Ci-Ren Tudeng
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Random Walk Model ◽  
And Diffusion

INTEGRO-DIFFERENTIAL EQUATIONS ASSOCIATED WITH CONTINUOUS-TIME RANDOM WALK

2013 ◽  
Vol 27 (12) ◽  
pp. 1330006 ◽  
Author(s):  
KWOK SAU FA ◽  
K. G. WANG
Keyword(s):  
Random Walk ◽  
Differential Equations ◽  
Continuous Time ◽  
Analytic Solutions ◽  
Continuous Time Random Walk ◽  
Kolmogorov Equation ◽  
Long Time ◽  
Intermediate Time ◽  
And Diffusion ◽  
Probability Density Function Pdf

The continuous-time random walk (CTRW) model is a useful tool for the description of diffusion in nonequilibrium systems, which is broadly applied in nature and life sciences, e.g., from biophysics to geosciences. In particular, the integro-differential equations for diffusion and diffusion-advection are derived asymptotically from the decoupled CTRW model and a generalized Chapmann–Kolmogorov equation, with generic waiting time probability density function (PDF) and external force. The advantage of the integro-differential equations is that they can be used to investigate the entire diffusion process i.e., covering initial-, intermediate- and long-time ranges of the process. Therefore, this method can distinguish the evolution detail for a system having the same behavior in the long-time limit but with different initial- and intermediate-time behaviors. An integro-differential equation for diffusion-advection is also presented for the description of the subdiffusive and superdiffusive regime. Moreover, the methods of solving the integro-differential equations are developed, and the analytic solutions for PDFs are obtained for the cases of force-free and linear force.

scholarly journals Generalized fractional Poisson process and related stochastic dynamics

2020 ◽  
Vol 23 (3) ◽  
pp. 656-693 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Alejandro P. Riascos
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Counting Process ◽  
Stochastic Dynamics ◽  
Waiting Times ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Fractional Operators ◽  
Fractional Poisson Process ◽  
Erlang Process

AbstractWe survey the ‘generalized fractional Poisson process’ (GFPP). The GFPP is a renewal process generalizing Laskin’s fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with admissible ranges 0 < β ≤ 1, α > 0 and a parameter characterizing the time scale. The GFPP involves Prabhakar generalized Mittag-Leffler functions and contains for special choices of the parameters the Laskin fractional Poisson process, the Erlang process and the standard Poisson process. We demonstrate this by means of explicit formulas. We develop the Montroll-Weiss continuous-time random walk (CTRW) for the GFPP on undirected networks which has Prabhakar distributed waiting times between the jumps of the walker. For this walk, we derive a generalized fractional Kolmogorov-Feller equation which involves Prabhakar generalized fractional operators governing the stochastic motions on the network. We analyze in d dimensions the ‘well-scaled’ diffusion limit and obtain a fractional diffusion equation which is of the same type as for a walk with Mittag-Leffler distributed waiting times. The GFPP has the potential to capture various aspects in the dynamics of certain complex systems.

Quartile histogram assessment of glioma malignancy using high b ‐value diffusion MRI with a continuous‐time random‐walk model

2021 ◽  
Vol 34 (4) ◽  
Author(s):  
M. Muge Karaman ◽  
Jiaxuan Zhang ◽  
Karen L. Xie ◽  
Wenzhen Zhu ◽  
Xiaohong Joe Zhou
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Diffusion Mri ◽  
B Value ◽  
Continuous Time Random Walk ◽  
Random Walk Model ◽  
High B Value

Multiscale Modeling of Carbonate Acidizing Using Continuous Time Random Walk Approach

2017 ◽  
Author(s):  
Kang Kang ◽  
Elsayed Abdelfatah ◽  
Maysam Pournik ◽  
Bor Jier Shiau ◽  
Jeffrey Harwell
Keyword(s):  
Random Walk ◽  
Multiscale Modeling ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Carbonate Acidizing
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