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Let $X$ be a square-integrable martingale. I am reading the following:

Let $\langle X \rangle_t$ be a Meyer process, i.e. the unique predictable process with $\langle X \rangle_0=0$ and right-continuous increasing paths such that $X^2-\langle X \rangle$ is a martingale.

Source: "Hedging of Non-Redundant Contingent Claims" by Föllmer and Sondermann, Contributions to Mathematical Economics , 1986

It is hard to find anything on "Meyer Process" on the web. Although it coincides with quadratic variation in the case where $X$ is a Brownian motion, I assume the Meyer process is not the same as quadratic variation? Does this process go under some other name nowadays?

  • I would say that "quadratic variation"" is this "other name" you are looking for. – saz Aug 17 '15 at 14:35
  • @saz I stumbled upon this: http://math.stackexchange.com/questions/902886/angle-bracket-and-sharp-bracket-for-discontinuous-processes It seems that they are not the same? –  Aug 17 '15 at 15:16
  • There are several notions of "quadratic variation", that's correct. However, since you require that $\langle X \rangle$ is predictable, the process has to coincide with the angle bracket $\langle X \rangle$ I introduced in my answer (because, by the Doob-Meyer decomposition, there exists a unique process with such properties). – saz Aug 17 '15 at 15:23

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