| Title: |
Optimal L2 -approximation of occupation and local times for symmetric stable processes |
| Authors: |
Altmeyer, Randolf; Le Guével, Ronan |
| Contributors: |
Faculty of mathematics Centre for Mathematical Sciences Cambridge (CMS); University of Cambridge Cambridge, UK (CAM); Université de Rennes (UR); Institut de Recherche Mathématique de Rennes (IRMAR); Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes); Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers; Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro); ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011) |
| Source: |
ISSN: 1935-7524. |
| Publisher Information: |
CCSD; Institute of Mathematical Statistics |
| Publication Year: |
2022 |
| Collection: |
Archive Ouverte de l'Université Rennes (HAL) |
| Subject Terms: |
Lévy process; lower bound; stable process; local time; occupation time; [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] |
| Description: |
International audience ; The L2-approximation of occupation and local times of a symmetric α-stable Lévy process from high frequency discrete time observations is studied. The standard Riemann sum estimators are shown to be asymptotically efficient when 0 < α ≤ 1, but only rate optimal for 1 < α ≤ 2. For this, the exact convergence of the L2-approximation error is proven with explicit constants. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/2108.11632; ARXIV: 2108.11632 |
| DOI: |
10.1214/22-EJS2013 |
| Availability: |
https://hal.science/hal-03324325; https://hal.science/hal-03324325v1/document; https://hal.science/hal-03324325v1/file/Estimation_occupation_time_stable_processes_HAL.pdf; https://doi.org/10.1214/22-EJS2013 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.A4528279 |
| Database: |
BASE |