2024/09/20 by Sonja Cox, Cox, Sonja, Joris van Winden +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #60G42 #60G60 #60H05 #60H15 #Advanced Harmonic Analysis Research #Applied mathematics #Combinatorics #FOS: Mathematics #Functional Analysis (math.FA) #Infimum and supremum #Insurance, Mortality, Demography, Risk Management #Mathematical economics #Mathematics #Probability (math.PR) #Pure mathematics #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2409.13615
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide sharp bounds for the supremum of countably many stochastic convolutions taking values in a 2-smooth Banach space. As a consequence, we obtain sharp bounds on the modulus of continuity of a family of stochastic integrals indexed by parameter x∈ M, where M is a metric space with finite doubling dimension. In particular, we obtain a theory of stochastic integration in Hölder spaces on arbitrary bounded subsets of ℝd. This is done by relating the (generalized) Hölder-seminorm associated with a modulus of continuity to a supremum over countably many variables, using a Kolmogorov-type chaining argument. We provide two applications of our results: first, we show long-term bounds for Ornstein-Uhlenbeck processes, and second, we derive novel results regarding the modulus of continuity of the parabolic Anderson model.