Probability Distributions Generated by Fractional Diffusion Equations
نویسنده
چکیده
Fractional calculus allows one to generalize the linear one-dimensional diiusion equation by replacing either the rst time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of these generalized diiusion equations are shown to provide probability density functions evolving in time or varying in space which are related to the special class of stable distributions. This property is a noteworthy generalization of what happens in the case of the standard diiusion equation and can be relevant in treating nancial and economical problems where stable probability distributions are known to play a key role.
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