Numerical Treatment of Homogeneous Semi-Markov Processes in Transient Case–a Straightforward Approach

Gianfranco Corradi (), Jacques Janssen () and Raimondo Manca ()
Additional contact information
Gianfranco Corradi: Universitá “La Sapienza”
Jacques Janssen: CESIAF
Raimondo Manca: Universitá “La Sapienza”

Methodology and Computing in Applied Probability, 2004, vol. 6, issue 2, 233-246

Abstract: Abstract This paper presents the numerical solution of the process evolution equation of a homogeneous semi-Markov process (HSMP) with a general quadrature method. Furthermore, results that justify this approach proving that the numerical solution tends to the evolution equation of the continuous time HSMP are given. The results obtained generalize classical results on integral equation numerical solutions applying them to particular kinds of integral equation systems. A method for obtaining the discrete time HSMP is shown by applying a very particular quadrature formula for the discretization. Following that, the problem of obtaining the continuous time HSMP from the discrete one is considered. In addition, the discrete time HSMP in matrix form is presented and the fact that the solution of the evolution equation of this process always exists is proved. Afterwards, an algorithm for solving the discrete time HSMP is given. Finally, a simple application of the HSMP is given for a real data social security example.

Keywords: semi-Markov processes; integral equations; numerical methods; algorithms; social insurance (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://link.springer.com/10.1023/B:MCAP.0000017715.28371.85 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:6:y:2004:i:2:d:10.1023_b:mcap.0000017715.28371.85

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1023/B:MCAP.0000017715.28371.85

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().