In this article, we construct pseudo random walks (symmetric and asymmetric) that converge in law to compositions of pseudoprocesses stopped at stable subordinators. We find the higher-order space-fractional heat-type equations whose fundamental solutions coincide with the law of the limiting pseudoprocesses. The fractional equations involve either Riesz operators or their Feller asymmetric counterparts. The main result of this article is the derivation of pseudoprocesses whose law is governed by heat-type equations of real-valued order gamma > 2. The classical pseudoprocesses are very special cases of those investigated here.
Pseudoprocesses Related to Space-Fractional Higher-Order Heat-Type Equations / Orsingher, Enzo; Toaldo, Bruno. - In: STOCHASTIC ANALYSIS AND APPLICATIONS. - ISSN 0736-2994. - STAMPA. - 32:4(2014), pp. 619-641. [10.1080/07362994.2014.911107]
Pseudoprocesses Related to Space-Fractional Higher-Order Heat-Type Equations
ORSINGHER, Enzo;TOALDO, BRUNO
2014
Abstract
In this article, we construct pseudo random walks (symmetric and asymmetric) that converge in law to compositions of pseudoprocesses stopped at stable subordinators. We find the higher-order space-fractional heat-type equations whose fundamental solutions coincide with the law of the limiting pseudoprocesses. The fractional equations involve either Riesz operators or their Feller asymmetric counterparts. The main result of this article is the derivation of pseudoprocesses whose law is governed by heat-type equations of real-valued order gamma > 2. The classical pseudoprocesses are very special cases of those investigated here.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.