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Stability of stochastic integrals under change of filtration

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  • Slud, Eric V.

Abstract

Let ([Omega],,P) be a probability space equipped with two filtrations {t} and {t} satisfying the usual conditions. Assume that X is a semimartingale and that h is locally bounded and predictable for each of the two filtrations {t} and {t}. New examples of such processes are given. Utilizing and extending partial results of Zheng (1982), this paper extends the available results on the relationship between the stochastic integral processes [integral operator]ths dXs taken respectively in the sense of {t} and of {t}. In particular, it is shown that these stochastic integrals differ at most by a continuous process with quadratic variation defined and equal to 0. If both stochastic integrals are {t[intersection]t} semimartingales, then it is proved that the stochastic integral [integral operator]ths dX s taken in {t} sense is indistinguishable from that taken in {t} sense.

Suggested Citation

  • Slud, Eric V., 1994. "Stability of stochastic integrals under change of filtration," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 221-233, April.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:2:p:221-233
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