The limit distribution of a singular sequence of Itô integrals. (English) Zbl 1496.60019
Chaumont, Loïc (ed.) et al., A lifetime of excursions through random walks and Lévy processes. A volume in honour of Ron Doney’s 80th birthday. Cham: Birkhäuser. Prog. Probab. 78, 83-86 (2021).
Summary: We give an alternative, elementary proof of a result of G. Pecati and M. Yor [Fields Inst. Commun. 44, 75–87 (2004; Zbl 1071.60017)] concerning the limit law of a sequence of Itô integrals with integrands having singular asymptotic behavior.
For the entire collection see [Zbl 1478.60005].
For the entire collection see [Zbl 1478.60005].
Citations:
Zbl 1071.60017References:
| [1] | Bell, D., Bolaños, R., Nualart, D.: Limit theorems for singular Skorohod integrals. Theory Probab. Math. Stat. In Publication (2021) · Zbl 1485.60053 |
| [2] | Nourdin, I.; Nualart, D.; Peccati, G., Quantitative stable limit theorems on the Wiener space, Ann. Probab., 44, 1, 1-41 (2016) · Zbl 1356.60035 · doi:10.1214/14-AOP965 |
| [3] | Peccati, G., Quantitative CLTs on a Gaussian space: a survey of recent developments, ESAIM: Proc., 44, 61-78 (2014) · Zbl 1327.60062 · doi:10.1051/proc/201444003 |
| [4] | Peccati, G., Yor, M.: Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge. In: Asymptotic Methods in Stochastics. Fields Institute Communication Series, pp. 75-87. AMS, Providence (2004) · Zbl 1071.60017 |
| [5] | Pratelli, L.; Rigo, P., Total variation bounds for Gaussian functionals, Stoch. Proc. Appl., 129, 7, 2231-2248 (2019) · Zbl 1415.60006 · doi:10.1016/j.spa.2018.07.005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
