A sharp maximal inequality for one-dimensional Dunkl martingales

Let X=(Xt)t≥0 be a one-dimensional Dunkl process of parameter k≥0, starting from 0. For any p≥1, we find the least constant Cp,k∈(0,∞] in the Doob-type inequality E(sup0≤t≤τXτ)p≤Cp,kE∣Xτ∣p where τ runs over all p/2-integrable stopping times of X. The proof exploits optimal stopping techniques....

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Bibliographic Details
Published in:Statistics & probability letters 2015-10, Vol.105, p.114-119
Main Author: Osȩkowski, Adam
Format: Article
Language:English
Subjects:
Best constant
Dunkl martingale
Maximal
Optimal stopping
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Summary:Let X=(Xt)t≥0 be a one-dimensional Dunkl process of parameter k≥0, starting from 0. For any p≥1, we find the least constant Cp,k∈(0,∞] in the Doob-type inequality E(sup0≤t≤τXτ)p≤Cp,kE∣Xτ∣p where τ runs over all p/2-integrable stopping times of X. The proof exploits optimal stopping techniques.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2015.06.008