Zobrazeno 1 - 6 of 6 pro vyhledávání: '"Jacobus J. Grobler"'
2
Itô's rule and Lévy's theorem in vector lattices
Autor: Coenraad C.A. Labuschagne, Jacobus J. Grobler
Publikováno v: Journal of Mathematical Analysis and Applications. 455:979-1004
The change of variable formula, or Ito's rule, is studied in a Dedekind complete vector lattice E with weak order unit E. Using the functional calculus we prove that for a Holder continuous semimartingale X t = X a + M t + B t , t ∈ J , and a twice
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ab3848a6ff3b9d2c117d5092bfcc4817
https://doi.org/10.1016/j.jmaa.2017.06.011
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3
The Itô integral for martingales in vector lattices
Autor: Jacobus J. Grobler, Coenraad C.A. Labuschagne
Publikováno v: Journal of Mathematical Analysis and Applications. 450:1245-1274
In the setting of a Dedekind complete Riesz space on which a conditional expectation is defined, we study the Ito integral. This integral obtains the integration of a stochastic process of a continuous parameter relative to a martingale. A considerab
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::38d6992d703f78bc232e81afed9fa46e
https://doi.org/10.1016/j.jmaa.2017.01.081
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4
Markov Processes, Strong Markov Processes and Brownian Motion in Riesz Spaces
Autor: Jacobus J. Grobler
Publikováno v: Trends in Mathematics ISBN: 9783030108496
The different definitions for Markov processes used in the classical case are studied in the abstract setting of vector lattices where they are not all equivalent. Strong Markov processes are defined and it is shown that a Brownian motion is a strong
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::367eff33cba34634ea132306ab91d93f
https://doi.org/10.1007/978-3-030-10850-2_10
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