For processes $X(t),t>0$ governed by signed measures whose density is the fundamental solution of third and fourth-order heat-type equations (higher-order diffusions) the explicit form of the joint distribution of $(\max_{0\leqs\leqt}X(s),X(t))$ is derived. The expressions presented include all results obtained so far and, for the third-order case, prove to be genuine probability distributions. The case of more general fourth-order equations is also investigated and the distribution of the maximum is derived.
Joint distributions of the maximum and the process for higher-order diffusions / Beghin, Luisa; Orsingher, Enzo; T., Ragozina. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 94:1(2001), pp. 71-93. [10.1016/s0304-4149(00)00105-8]
Joint distributions of the maximum and the process for higher-order diffusions
BEGHIN, Luisa;ORSINGHER, Enzo;
2001
Abstract
For processes $X(t),t>0$ governed by signed measures whose density is the fundamental solution of third and fourth-order heat-type equations (higher-order diffusions) the explicit form of the joint distribution of $(\max_{0\leqs\leqt}X(s),X(t))$ is derived. The expressions presented include all results obtained so far and, for the third-order case, prove to be genuine probability distributions. The case of more general fourth-order equations is also investigated and the distribution of the maximum is derived.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
