Issue |
ESAIM: PS
Volume 26, 2022
|
|
---|---|---|
Page(s) | 378 - 396 | |
DOI | https://doi.org/10.1051/ps/2022011 | |
Published online | 24 November 2022 |
On optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes
1
University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
2
Warsaw School of Economics, al. Niepodległości 162, 02-554 Warszawa, Poland
* Corresponding author: rlocho@sgh.waw.pl
Received:
13
October
2020
Accepted:
27
October
2022
For a general càdlàg Lévy process X on a separable Banach space V we estimate values of infc≥0 {ψ(c) + infY∈AX(c) 𝔼TV(Y,[0,T])}, where AX(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 ℝd and a symmetric α-stable process (α ∈ (1, 2)) on ℝ.
Mathematics Subject Classification: 60G51 / 60G52 / 60J65 / 49K45
Key words: Levy processes / total variation / uniform approximation
© The authors. Published by EDP Sciences, SMAI 2022
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