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Semi-additive functionals of semi-Markov processes and measure-valued Poisson equation.
- Source :
-
Statistics & Probability Letters . Apr2019, Vol. 147, p45-56. 12p. - Publication Year :
- 2019
-
Abstract
- Abstract In this paper, we consider a continuous-time semi-Markov process (SMP) in Polish spaces. We first introduce the semi-additive functional in semi-Markov cases, a natural generalization of the additive functional of Markov process (MP). The main contribution of this paper is the properties of semi-additive functional aforementioned. First, semi-additive functionals of SMPs are characterized in terms of a càdlàg function with zero initial value and a measurable function. Second, the necessary and sufficient conditions are investigated under which a semi-additive functional of SMP is a semimartingale, a local martingale, or a special semimartingale respectively. By the way, the Itô type formula is given. Finally, we study the expected cumulative discounted value of the semi-additive functional of an SMP. We prove that it solves a measure-valued Poisson equation and give the uniqueness conditions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01677152
- Volume :
- 147
- Database :
- Academic Search Index
- Journal :
- Statistics & Probability Letters
- Publication Type :
- Periodical
- Accession number :
- 134088150
- Full Text :
- https://doi.org/10.1016/j.spl.2018.11.004