Continuous Time Random Walk: Difference between revisions

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In standard CTRW theory, it is customary to assume that the single particle step distribution is ''separable'', i.e., that ''Δx'' is independent from ''Δt'', so that
In standard CTRW theory, it is customary to assume that the single particle step distribution is ''separable'', i.e., that ''Δx'' is independent from ''Δt'', so that


: <math>\xi( \Delta x, \Delta t; x,t) = p(\Delta x; x,t) \psi(\Delta t; x,t)</math>
: <math>\xi( \Delta x, \Delta t; x,t) = p(\Delta x; x,t+\Delta t) \psi(\Delta t; x,t)</math>


In addition, homogeneity in space and time is assumed (i.e., ''p'' and ''&psi;'' do not depend on ''x'' and ''t''). However, recently it was shown that a Master Equation can also be derived in the case that ''p'' depends on ''x'' and ''t'', while ''&psi;'' depends on ''x'' (but not ''t'').
In addition, homogeneity in space and time is assumed (i.e., ''p'' and ''&psi;'' do not depend on ''x'' and ''t''). However, recently it was shown that a Master Equation can also be derived in the case that ''p'' depends on ''x'' and ''t'', while ''&psi;'' depends on ''x'' (but not ''t'').

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