For a general càdlàg Lévy process X on a separable Banach space V we estimate values of infc≥0 {ψ(c) + inf$$ 𝔼TV(Y,[0,T])}, where A$$(c) is the family of processes on V adapted to the natural filtration of X, a.s. approximating paths of X uniformly with accuracy c, ψ is a penalty function with polynomial growth and TV(Y, [0,T]) denotes the total variation of the process Y on the interval [0,T], Next, we apply obtained estimates in three specific cases: Brownian motion with drift on ℝ, standard Brownian motion on ℝ$$ and a symmetric α-stable process (α ∈ (1, 2)) on ℝ.
Keywords: Levy processes, total variation, uniform approximation
@article{PS_2022__26_1_378_0,
author = {Bednorz, Witold M. and {\L}ochowski, Rafa{\l} M. and Martynek, Rafa{\l}},
title = {On optimal uniform approximation of {L\'evy} processes on {Banach} spaces with finite variation processes},
journal = {ESAIM: Probability and Statistics},
pages = {378--396},
year = {2022},
publisher = {EDP-Sciences},
volume = {26},
doi = {10.1051/ps/2022011},
mrnumber = {4513264},
zbl = {1523.60087},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2022011/}
}
TY - JOUR AU - Bednorz, Witold M. AU - Łochowski, Rafał M. AU - Martynek, Rafał TI - On optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes JO - ESAIM: Probability and Statistics PY - 2022 SP - 378 EP - 396 VL - 26 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2022011/ DO - 10.1051/ps/2022011 LA - en ID - PS_2022__26_1_378_0 ER -
%0 Journal Article %A Bednorz, Witold M. %A Łochowski, Rafał M. %A Martynek, Rafał %T On optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes %J ESAIM: Probability and Statistics %D 2022 %P 378-396 %V 26 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2022011/ %R 10.1051/ps/2022011 %G en %F PS_2022__26_1_378_0
Bednorz, Witold M.; Łochowski, Rafał M.; Martynek, Rafał. On optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes. ESAIM: Probability and Statistics, Tome 26 (2022), pp. 378-396. doi: 10.1051/ps/2022011
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