A BDG inequality for stochastic Volterra integrals

2025/03/31 by Alexandre Pannier, Pannier, Alexandre
Economics, Econometrics and Finance · Decision Sciences · Business, Management and Accounting · #Stochastic processes and financial applications #Risk and Portfolio Optimization #Advanced Queuing Theory Analysis

paper · pdf · doi:10.48550/arxiv.2503.24252

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 L^γ-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 uniform-in-time bounds for mean-reverting stochastic Volterra equations. Finally, we compare our findings with existing results in the literature.

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