摘要
In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented.
In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented.
作者
Enzo Orsingher, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università degli Studi di Roma "La Sapienza", Piazzale Aldo Moro, 5-00185 Roma, ItalyE-mail: orsinghe@pow2.sta.uniromal.itXuelei Zhao, Institute of Applied Mathematics, University of Bonn, Bonn 53115, GermanyE-mail: zhao@wiener. iam. uni-bonn, deInstitute of Mathematics, Shantou University, Shantou 515063, P. R. ChinaE-mail: xlzhao@mailserv.stu, edu. cn
基金
This work is partially supported by the Natural Science Foundation of Guangdong Province
National Natural Science Foundation of China grant No. 19501026
the Alexander yon Humbodlt Foundation
