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This article is cited in 19 scientific papers (total in 19 papers)
Stochastic integration on the real line
A. Basse-O'Connora, S.-E. Graversenb, J. Pedersenb a The University of Tennessee
b University of Aarhus, Department of Mathematical Sciences
Abstract:
Stochastic integration on the predictable $\sigma$-field with respect to increment semimartingales, and, more generally, $\sigma$-finite $L^0$-valued measures is studied. The latter are also known as formal semimartingales. In particular, the triplet of $\sigma$-finite measures is introduced and used to characterize the set of integrable processes. Special attention is given to Lévy processes indexed by the real line. Surprisingly, many of the basic properties break down in this situation compared to the usual $\mathbf{R}_+$ case. The results enable us to define, represent, and study different classes of stationary processes.
Keywords:
stochastic integration; (increment) semimartingales; Lévy processes.
Received: 02.08.2011 Revised: 14.06.2012
Citation:
A. Basse-O'Connor, S.-E. Graversen, J. Pedersen, “Stochastic integration on the real line”, Teor. Veroyatnost. i Primenen., 58:2 (2013), 355–380; Theory Probab. Appl., 58:2 (2014), 193–215
Linking options:
https://www.mathnet.ru/eng/tvp4510https://doi.org/10.4213/tvp4510 https://www.mathnet.ru/eng/tvp/v58/i2/p355
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Abstract page: | 502 | Full-text PDF : | 244 | References: | 91 | First page: | 3 |
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