We propose a theory of stochastic integration with respect to a sequence of semimartingales. 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 “Mémin’s theorem”, but it also presents some “bad properties”, which will be pointed out by some examples.
De Donno, M., M., P., Stochastic integration with respect to a sequence of semimartingales, Lecture Notes in Mathematics. Seminaire de Probabilites XXXIX, Springer, Berlin 2006 1874: 121-137. 10.1007/978-3-540-35513-7_10 [http://hdl.handle.net/10807/168922]
Stochastic integration with respect to a sequence of semimartingales
De Donno, Marzia;
2006
Abstract
We propose a theory of stochastic integration with respect to a sequence of semimartingales. 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 “Mémin’s theorem”, but it also presents some “bad properties”, which will be pointed out by some examples.
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