Abstract
On définit un processus à deux indices α et β par intégration fractionnaire d'un bruit blanc. On démontre qu'il est auto-similaire et à accroissements stationnaires, les accroissements étant rectangulaires. On donne quelques propriétés de régularité des trajectoires et la continuité du processus par rapport aux deux paramètres. On obtient un champ aléatoire gaussien de même loi que celui proposé par Anna Kamont, mais notre définition permet de montrer d'autres propriétés, en particulier trajectorielles, et conduit plus aisément à des algorithmes de simulation de tels champs.
A random field depending on two parameters α and β is defined by a fractional integration with respect to the white noise field. Such a process is autosimilar with stationary rectangular increments. The paths have some regular properties, and the process has a sort of regularity with respect of the parameters. The process has the same law as that of Anna Kamont. However, our definition allows to prove some others properties, particularly paths properties, and gives easily simulation algorithms of such of fields.
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Ayache, A., Leger, S. & Pontier, M. Drap brownien fractionnaire. Potential Analysis 17, 31–43 (2002). https://doi.org/10.1023/A:1015260803576
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DOI: https://doi.org/10.1023/A:1015260803576