【摘 要】
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We briefly recall the origin,history and some physical applications (fractional Fokker-Planck equation) of Levy stable probability distributions.We report on recent findings of exact and explicit expr
【机 构】
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Polish Academy of Sciences, Poland
【出 处】
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The XXIX International Colloquium on Group-Theoretical Metho
论文部分内容阅读
We briefly recall the origin,history and some physical applications (fractional Fokker-Planck equation) of Levy stable probability distributions.We report on recent findings of exact and explicit expressions for one-sided (0 < α < 1) and two-sided (1 < α ≤ 2) Levy stable densities g α (x),of index α for all α =l/k,with k and l positive integers.We shall exemplify analytically and graphically several examples of known,and an infinite ensemble of new formulae for such distributions.We observe that the one- and two-sided Levy density can be obtained via so-called Levy2 transform L(2) α,which satisfy the semigroup properties.
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