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with jumps of infinite variation. Despite such non-uniqueness, the terminology "pure-jump Lévy process" is in common use to denote the subset of Lévy processes whose continuous quadratic variation is zero (i.e., those Lévy processes that have no Brownian motion component). One may also speak of pure-jump processes in the stricter sense of being equal to the sum of their jumps. This is certainly possible if the jumps are of finite variation but sometimes even

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