Generalized Poisson measures on topological spaces and applications. Issue 3 (4th May 2021)

• Record Type: Journal Article
• Authors: Al-Obaidi, Ali H. M.; Dshalalow, Jewgeni H.
• Is Part Of: Stochastic analysis and applications. Volume 39:Issue 3(2021)
• Page Start: 525
• Page End: 548
• Publication Date: 2021-05-04
• Subjects: Poisson random measure -- stochastic intensities -- modulation -- Campbell's formula -- stochastic finance -- semi-Markov modulated random measures -- stochastic control; 28Axx -- 60G57 -- 60G55 -- 60Hxx -- 60H05; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1810070
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We introduce and study a marked Poisson random measure on a σ -compact Hausdorff space. The underlying parameters of this measure are changing in accordance with the evolution of some stochastic process. This random measure (also known as a modulated measure) resembles those of the conventional Poisson random measure. Among many applications, the one about Poisson random measures modulated by semi-Markov processes found in stochastic finance.