Journal of Stochastic Analysis
Abstract
We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval, the upper bound depends linearly on the Lγ-norm of the kernel, for any γ > 2. We demonstrate the utility of this inequality in quantifying the pathwise distance between two stochastic Volterra equations with distinct kernels, with a particular emphasis on the multifactor Markovian approximation. For kernels that decay sufficiently fast, we derive an alternative inequality valid over an infinite time interval, providing uniformin- time bounds for mean-reverting stochastic Volterra equations. Finally, we compare our findings with existing results in the literature.
Recommended Citation
Pannier, Alexandre
(2025)
"A BDG INEQUALITY FOR STOCHASTIC VOLTERRA INTEGRALS,"
Journal of Stochastic Analysis: Vol. 6:
No.
3, Article 1.
DOI: 10.31390/josa.6.3.01
Available at:
https://repository.lsu.edu/josa/vol6/iss3/1
DOI
10.31390/josa.6.3.01