2012/09/20 by Qi Feng, Feng, Qi, Xuejing Zhang +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1209.4624
openalex publication_date 2012/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study the Taylor expansion for the solutions of differential equations driven by p-rough paths with p>2. We prove a general theorem concerning the convergence of the Taylor expansion on a nonempty interval provided that the vector fields are analytic on a ball centered at the initial point. We also derive criteria that enable us to study the rate of convergence of the Taylor expansion. Finally and this is also the main and the most original part of this paper, we prove Castell expansions and tail estimates with exponential decays for the remainder terms of the solutions of the stochastic differential equations driven by continuous centered Gaussian process with finite 2D~ρ-variation and fractional Brownian motion with Hurst parameter H>1/4.