Distributional representations and dominance of a Lévy process over its maximal jump processes
Distributional identities for a Lévy process Xt , its quadratic variation process Vt and its maximal jump processes, are derived, and used to make “small time” (as t ↓ 0) asymptotic comparisons between them. The representations are constructed using properties of the underlying Poisson point process of the jumps of X. Apart from providing insight into the connections between X, V , and their maximal jump processes, they enable investigation of a great variety of limiting behaviours. As an...[Show more]
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