E. Orsingher, M. D'Ovidio
For the fundamental solutions of heat-type equations of order n we give a general stochastic representation in terms of damped oscillations with generalized gamma distributed parameters. By composing the pseudo-process X of order n (related to the higher-order heat-type equation of order n) with positively skewed stable r.v.'s we obtain genuine r.v.'s whose explicit distribution is given in terms of Cauchy asymmetric laws for n=3. The pseudo process X composed with n-times iterated positively skewed stable r.v.'s is shown to have stable asymmetric distribution.
Pseudo-process, higher-order heat equation, Airy functions, Cauchy distribution, stable laws, fractional di usion equations
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