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EnglishWe propose a theory of stochastic integration with respect to a sequence of semimartingales, starting from the theory of cylindrical integration with respect to a sequence of square-integrable martingales and with respect to a sequence of processes with finite variation. Indeed, by making use of an appropriate change in probability, we replace the integral with respect to a sequence of semimartingales with the sum of an integral with respect to a sequence of square integrable martingales and an integral with respect to a sequence of predictable processes with integrable variation. We show that, with our definition, the stochastic integral keeps some good properties of the integral with respect to a finite-dimensional semimartingale, such as invariance with respect to a change in probability and the so-called ``Memin's theorem". There are however some differences with the finite-dimensional case, and some ``bad properties'', which are pointed out by some examples.
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| Titolo: | Stochastic integration with respect to a sequence of semimartingales |
| Data di pubblicazione: | 2006 |
| Autori: | |
| Autori: | DE DONNO, Marzia; M., Pratelli |
| Rivista: | LECTURE NOTES IN MATHEMATICS |
| Abstract: | We propose a theory of stochastic integration with respect to a sequence of semimartingales, starting from the theory of cylindrical integration with respect to a sequence of square-integrable martingales and with respect to a sequence of processes with finite variation. Indeed, by making use of an appropriate change in probability, we replace the integral with respect to a sequence of semimartingales with the sum of an integral with respect to a sequence of square integrable martingales and an integral with respect to a sequence of predictable processes with integrable variation. We show that, with our definition, the stochastic integral keeps some good properties of the integral with respect to a finite-dimensional semimartingale, such as invariance with respect to a change in probability and the so-called ``Memin's theorem". There are however some differences with the finite-dimensional case, and some ``bad properties'', which are pointed out by some examples. |
| Appare nelle tipologie: | 01 - Article in academic journal / Articolo su rivista Scientifica |
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