scholarly journals Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations

2018 ◽  
Vol 256 (1228) ◽  
pp. 0-0 ◽  
Author(s):  
Nawaf Bou-Rabee ◽  
Eric Vanden-Eijnden
Keyword(s):  
Differential Equations ◽  
Random Walks ◽  
Numerical Solution ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Continuous Time Random Walks

Heterogeneous Memorized Continuous Time Random Walks in an External Force Fields

2014 ◽  
Vol 156 (6) ◽  
pp. 1111-1124 ◽  
Author(s):  
Jun Wang ◽  
Ji Zhou ◽  
Long-Jin Lv ◽  
Wei-Yuan Qiu ◽  
Fu-Yao Ren
Keyword(s):  
Random Walks ◽  
External Force ◽  
Continuous Time ◽  
Force Fields ◽  
Continuous Time Random Walks

scholarly journals Clustered continuous-time random walks: diffusion and relaxation consequences

2012 ◽  
Vol 468 (2142) ◽  
pp. 1615-1628 ◽  
Author(s):  
Karina Weron ◽  
Aleksander Stanislavsky ◽  
Agnieszka Jurlewicz ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Continuous Time ◽  
Waiting Times ◽  
Scaling Limit ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
The Novel ◽  
Fractional Diffusion Equations ◽  
Continuous Time Random Walks

We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.

Continuous time random walks and heat transfer in porous media

2006 ◽  
Vol 67 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Simon Emmanuel ◽  
Brian Berkowitz
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Random Walks ◽  
Continuous Time ◽  
Continuous Time Random Walks
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