4,427
edits
Continuous Time Random Walk: Difference between revisions
→The Master Equation
| Line 39: | Line 39: | ||
:<math>K( \Delta x, \Delta t; x,t) = p(\Delta x; x,t+\Delta t) \phi(\Delta t; x)</math> | :<math>K( \Delta x, \Delta t; x,t) = p(\Delta x; x,t+\Delta t) \phi(\Delta t; x)</math> | ||
The GME is an integro-differential equation, | The GME is an integro-differential equation, generalizing the usual (partial differential) equations for transport. | ||
The particle flux at any point in space depends on the global distribution of the transported particle density field, and on its history (although the history dependence can be eliminated by choosing a Markovian waiting time distribution). | |||
The treatment of boundary conditions in a GME is different from standard differential equations. <ref>[http://dx.doi.org/10.1088/1751-8113/41/21/215004 B.Ph. van Milligen, I. Calvo, and R. Sánchez, ''Continuous time random walks in finite domains and general boundary conditions: some formal considerations'', J. Phys. A: Math. Theor. '''41''' (2008) 215004]</ref> | The treatment of boundary conditions in a GME is different from standard differential equations. <ref>[http://dx.doi.org/10.1088/1751-8113/41/21/215004 B.Ph. van Milligen, I. Calvo, and R. Sánchez, ''Continuous time random walks in finite domains and general boundary conditions: some formal considerations'', J. Phys. A: Math. Theor. '''41''' (2008) 215004]</ref> | ||