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Summable processes versus semimartingales


Authors: Nicolae Dinculeanu and Oana Mocioalca
Journal: Proc. Amer. Math. Soc. 132 (2004), 3089-3095
MSC (2000): Primary 60H05; Secondary 60G20
DOI: https://doi.org/10.1090/S0002-9939-04-07308-3
Published electronically: May 20, 2004
MathSciNet review: 2063131
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Abstract | References | Similar Articles | Additional Information

Abstract: The classical stochastic integral $\int H dX$ is defined for real-valued semimartingales $X$. For processes with values in a Banach space $E$, the stochastic integral $\int H dX$ is defined for locally summable processes $X$, using a measure-theoretical approach.

We investigate the relationship between semimartingales and locally summable processes.

A real-valued, locally summable process is a special semimartingale. We prove that in infinite-dimensional Banach spaces, a locally summable process is not necessarily a semimartingale.


References [Enhancements On Off] (What's this?)

  • [B-D] J. K. Brooks and N. Dinculeanu, Stochastic Integration in Banach Spaces, Seminar on Stochastic Processes, Birkhäuser, Boston, 1991, 27-115.
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  • [D] N. Dinculeanu, Vector Integration and Stochastic Integration in Banach Spaces, Wiley, New York, 2000. MR 2001h:60096
  • [K] A. U. Kussmaul, Stochastic integration and Generalized Martingales, Pitman, London, 1977. MR 58:7841

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Additional Information

Nicolae Dinculeanu
Affiliation: Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, Florida 32611–8105
Email: nd@math.ufl.edu

Oana Mocioalca
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
Email: oana@math.purdue.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07308-3
Keywords: Summable processes, semimartingale, integrable variation, integrable semivariation, local martingale, dual projection.
Received by editor(s): August 27, 2002
Published electronically: May 20, 2004
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2004 American Mathematical Society

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