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Continuous Time Random Walk: Difference between revisions
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→The Master Equation
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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 ''ψ'' 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 ''ψ'' depends on ''x'' (but not ''t''). | In addition, homogeneity in space and time is assumed (i.e., ''p'' and ''ψ'' 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 ''ψ'' depends on ''x'' (but not ''t''). | ||