Taylor expansions and Castell estimates for solutions of stochastic differential equations driven by rough paths

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 $2D~\rho-$variation and fractional Brownian motion with Hurst parameter $H>1/4$.Comment: Final version for publis

An Analysis On Causes Of Late Final Payment And Release Of Retainage: Electrical Subcontractors’ View

Using the survey approach, this study identified the underlying causes of late payments and release of retainage for electrical subcontractors, attempting to answer the questions, What were the minimum, maximum and average delay days of final payment and release of retainage? , What were the rank of factors in terms of significance on delaying final payment and release of retainage? , and What were the rank of factors in terms of frequency on delaying final payment and release of retainage? A survey questionnaire was developed and distributed to about 150 professionals in electrical subcontractors. 29 reports were collected. Based upon the analysis of data, the mean value and most common value of minimum, maximum, and average delay days were concluded. Also, a detailed analysis on the significance and frequency of each factors were conducted. The contribution includes ranks of factors based on significance and frequency in terms of delaying final payment and retainage, and suggestions to improve cash efficiency for electrical subcontractors