Moment estimates for Lévy Processes
By Harald Luschgy, Gilles Pagès. 2006
48 citations recorded by the source corpus.
For real Levy processes $(X_t)_{t \geq 0}$ having no Brownian component with Blumenthal-Getoor index $\beta$, the estimate $E \sup_{s \leq t} |X_s - a_p s|^p \leq C_p t$ for every $t \in [0,1]$ and suitable $a_p \in R$ has been established by Millar for $\beta 2$ and $p \leq\beta$.
Subfields: Finance, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b4005ee6b2b2750c997f111f743bebe20f9a9235
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Citations in the corpus
- Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, background): “However, different from the drifted Wiener process, the sequence {n−1/2∂βQn(θ0)} does not converge because (h−1/2 n jX)j≤n cannot be L -bounded for large q > 2 as can be seen from the moment structure of Lévy processes; see Luschgy and Pagès [24] for general moment estimates in small time with sever”
- Statistical inference for time-changed Lévy processes via composite characteristic function estimation (2010, unknown): “(6.5) Moreover, under assumption (AL2) [see Luschgy and Pagès (2008)]∫ |x|mpk,t (x) dx = O(t), ∫ |x|mpl,t (x) dx = O(t), t → 0,(6.6) and ∫ |x|mpk,t (x) dx = O(tm), (6.7) ∫ |x|mpl,t (x) dx = O(tm), t → +∞, for any 2 ≤ m ≤ p.”