PreprintCC BY 4.0arXiv
Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations
Abstract
We bound the difference between two stochastic Volterra processes with identical Lipschitz coefficients but different kernels. For non-convolution kernels, we establish estimates in C0([0,T];Lp(Ω)), p≥ 2, and for convolution kernels in Lp(Ω;Lq(0,T)), q ∈ [1,p], and Cβ([0,T];Lp(Ω)), Lp(Ω;Cβ([0,T])), where the range of the Hölder exponent β∈ (0,1] is the maximal permitted by the regularity of the processes. For the fractional kernel, we then construct Markovian approximations whose error we show to decay as e−a√N in the aforementioned norms, using an N-node quadrature based on sinc methods. Numerical experiments for the fractional Brownian motion verify our findings.
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BibTeX
@misc{corneille2026convergence,
title = {{Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations}},
author = {Noé Corneille and Kristin Kirchner and Pietro Pezzoli Frigerio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17472},
eprint = {2609.17472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17472},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations
AU - Noé Corneille
AU - Kristin Kirchner
AU - Pietro Pezzoli Frigerio
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17472
UR - https://arxiv.org/abs/2609.17472
AB - We bound the difference between two stochastic Volterra processes with identical Lipschitz coefficients but different kernels. For non-convolution kernels, we establish estimates in C^0([0,T];L^p(Ω)), p≥ 2, and for convolution kernels in L^p(Ω;L^q(0,T)), q ∈ [1,p], and C^β([0,T];L^p(Ω)), L^p(Ω;C^β([0,T])), where the range of the Hölder exponent β∈ (0,1] is the maximal permitted by the regularity of the processes. For the fractional kernel, we then construct Markovian approximations whose error we show to decay as e^−a√N in the aforementioned norms, using an N-node quadrature based on sinc methods. Numerical experiments for the fractional Brownian motion verify our findings.
ER -