The conditional Feynman-Kac functional is used to derive the Laplace transforms of conditional maximum distributions of processes related to third- and fourth-order equations. These distributions are then obtained explicitly and are expressed in terms of stable laws and the fundamental solutions of these higher-order equations. Interestingly, it is shown that in the third-order case, a genuine non-negative real-valued probability distribution is obtained. (C) 2000 Elsevier Science B.V. All rights reserved.
Conditional maximal distributions of processes related to higher-order heat-type equations / Beghin, Luisa; Kenneth J., Hochberg; Orsingher, Enzo. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 85:2(2000), pp. 209-223. [10.1016/s0304-4149(99)00074-5]
Conditional maximal distributions of processes related to higher-order heat-type equations
BEGHIN, Luisa;ORSINGHER, Enzo
2000
Abstract
The conditional Feynman-Kac functional is used to derive the Laplace transforms of conditional maximum distributions of processes related to third- and fourth-order equations. These distributions are then obtained explicitly and are expressed in terms of stable laws and the fundamental solutions of these higher-order equations. Interestingly, it is shown that in the third-order case, a genuine non-negative real-valued probability distribution is obtained. (C) 2000 Elsevier Science B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
