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We know that any Semimartingale has Quadratic variation. I am interested to know if the converse is also true i.e. if a process has quadratic variation then it is semimartingale. Can some one prove/disprove it. Thank you very much.

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Hi if you take any process that is not a semi-martingale with null quadratic variations (for example a fractional Brownian motion with Hurst parameter less than 1/2) and then you add some jumps, then it has non null quadratic variations (the square of its jumps) and you have a counterexample.

Best regards

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  • $\begingroup$ fBm with H<1/2 has infinite quadratic variation $\endgroup$
    – user658409
    Commented Jul 16, 2019 at 6:50

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