Summary
This work is devoted to prove the following fact: Suppose thatΦ is a nuclear space whose dualΦ′ is nuclear under the strong topology. IfX′ is a weakly adapted mapping with values inΦ′ such that for anyφεΦ,X'(φ) has a modification which is a semimartingale then there exists a unique projective system of Hubert space-valued semimartingales indexed by the Hilbert-Schmidt neighbourhood base of the dual space whose “projective limit” isX′.
In the last part we study in detail a semimartingale defined as the convolution of a distribution by a random Dirac measure whose support is determined by the trajectories of a real-valued semimartingale.
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Ustunel, A.S. A characterization of semimartingales on nuclear spaces. Z. Wahrscheinlichkeitstheorie verw Gebiete 60, 21–39 (1982). https://doi.org/10.1007/BF01957095
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DOI: https://doi.org/10.1007/BF01957095