dc.contributor.author | Grobler, Jacobus J. | |
dc.contributor.author | Labuschagne, Coenraad C.A. | |
dc.date.accessioned | 2017-03-15T07:27:00Z | |
dc.date.available | 2017-03-15T07:27:00Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Grobler, J.J. & Labuschagne, C.C.A. 2017. The quadratic variation of continuous time stochastic processes in vector lattices. Journal of mathematical analysis and applications, 450(1):314-329. [https://doi.org/10.1016/j.jmaa.2017.01.034] | en_US |
dc.identifier.issn | 0022-247X | |
dc.identifier.uri | http://hdl.handle.net/10394/20828 | |
dc.identifier.uri | https://doi.org/10.1016/j.jmaa.2017.01.034 | |
dc.identifier.uri | https://www.sciencedirect.com/science/article/pii/S0022247X17300562 | |
dc.description.abstract | We define and study order continuity, topological continuity, γ-Hölder-continuity and Kolmogorov–Čentsov-continuity of continuous-time stochastic processes in vector lattices and show that every such kind of continuous submartingale has a continuous compensator of the same kind. The notion of variation is introduced for continuous time stochastic processes and for a γ-Hölder-continuous martingale with finite variation, we prove that it is a constant martingale. The localization technique for not necessarily bounded martingales is introduced and used to prove our main result which states that the quadratic variation of a continuous-time γ-Hölder continuous martingale X is equal to its compensator 〈X〉 | en_US |
dc.language.iso | en | en_US |
dc.publisher | Elsevier | en_US |
dc.subject | Martingale | en_US |
dc.subject | Quadratic variation | en_US |
dc.subject | Stochastic process | en_US |
dc.subject | Stopping time | en_US |
dc.subject | Vector lattice | en_US |
dc.title | The quadratic variation of continuous time stochastic processes in vector lattices | en_US |
dc.type | Article | en_US |
dc.contributor.researchID | 10173501 - Grobler, Jacobus Johannes | |