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Continuous Time Random Walk: Difference between revisions
→Fractional Differential Equations
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To obtain the fractional differential operators, it is necessary to make an assumption regarding the shape of the distributions appearing in the kernel ''K''. Invoking the Generalized Limit Theorem for the sums of random variables, | To obtain the fractional differential operators, it is necessary to make an assumption regarding the shape of the distributions appearing in the kernel ''K''. Invoking the Generalized Limit Theorem for the sums of random variables, | ||
<ref>B. V. Gnedenko and A. N. Kolmogorov, ''Limit Distributions of Sums of Independent Random Variables'', Addison-Wesley, Reading, MA (1954)</ref> | <ref>B. V. Gnedenko and A. N. Kolmogorov, ''Limit Distributions of Sums of Independent Random Variables'', Addison-Wesley, Reading, MA (1954)</ref> | ||
these distributions are taken to be Lévy distributions. | these distributions are taken to be [[:Wikipedia:Stable_distribution|Lévy distributions]]. | ||
While the step distribution can be any Lévy distribution, the waiting time distribution must be ''positive extremal'', since Δ''t'' > 0. | While the step distribution can be any Lévy distribution, the waiting time distribution must be ''positive extremal'', since Δ''t'' > 0. | ||
This choice allows modelling both | This choice allows modelling both | ||