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dc.contributor.authorGrobler, Jacobus J.
dc.contributor.authorLabuschagne, Coenraad C.A.
dc.identifier.citationGrobler, 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. []en_US
dc.description.abstractWe 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.subjectQuadratic variationen_US
dc.subjectStochastic processen_US
dc.subjectStopping timeen_US
dc.subjectVector latticeen_US
dc.titleThe quadratic variation of continuous time stochastic processes in vector latticesen_US
dc.contributor.researchID10173501 - Grobler, Jacobus Johannes

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