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-m related to the higher-order heat-type equation with positively skewed stable r.v.'s T-1/3(j), j = 1, 2, . . . , n we obtain genuine r.v.'s whose explicit distribution is given for n = 3 in terms of Cauchy asymmetric laws. We also prove that X-3 (T-1/3(1) (. . . (T-1/3(n) (t)) . . .)) has a stable asymmetric law.

Probabilistic representation of fundamental solutions to partial derivative u/partial derivative t = K-m partial derivative(m)u/partial derivative x(m) / Orsingher, Enzo; D'Ovidio, Mirko. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - ELETTRONICO. - 17:0(2012), pp. 1-12. [10.1214/ecp.v17-1885]

Probabilistic representation of fundamental solutions to partial derivative u/partial derivative t = K-m partial derivative(m)u/partial derivative x(m)

ORSINGHER, Enzo;D'OVIDIO, MIRKO
2012

Abstract

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-m related to the higher-order heat-type equation with positively skewed stable r.v.'s T-1/3(j), j = 1, 2, . . . , n we obtain genuine r.v.'s whose explicit distribution is given for n = 3 in terms of Cauchy asymmetric laws. We also prove that X-3 (T-1/3(1) (. . . (T-1/3(n) (t)) . . .)) has a stable asymmetric law.
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/480486
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 12
social impact