2012/06/26 by Sebastian Riedel, Riedel, Sebastian, Weijun Xu +1
Economics, Econometrics and Finance · Environmental Science · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Probability (math.PR) #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1206.5866
20 pages, updated abstract and introduction
openalex publication_date 2012/06/26 · arxiv created 2012/08/02 · arxiv updated 2012/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have been obtained recently in [Friz-Riedel, AIHP, to appear]. One advantage of our argument is that we obtain the bound for the third level iterated integrals merely based on the first two levels, and this reflects the intrinsic nature of rough paths. Our estimates are sharp when both covariance functions have finite 1-variation, which includes a large class of Gaussian processes. Two applications of our estimates are discussed. The first one gives the a.s. convergence rates for approximated solutions to rough differential equations driven by Gaussian processes. In the second example, we show how to recover the optimal time regularity for solutions of some rough SPDEs.