Averaging principle for McKean-Vlasov SDEs driven by multiplicative fractional noise with highly oscillatory drift coefficient

In this paper, we study averaging principle for a class of McKean-Vlasov stochastic differential equations (SDEs) that contain multiplicative fractional noise with Hurst parameter $H >$ 1/2 and highly oscillatory drift coefficient. Here the integral corresponding to fractional Brownian motion is the generalized Riemann-Stieltjes integral. Using Khasminskii's time discretization techniques, we prove that the solution of the original system strongly converges to the solution of averaging system as the times scale $\epsilon$ gose to zero in the supremum- and H\"older-topologies which are sharpen existing ones in the classical Mckean-Vlasov SDEs framework.Comment: 12 page

Research Of E-Commerce Enterprises Capability Maturity Theory And Initial Model Construction

With the constant development and evolution of “Internet+” strategic thinking, the electronic commerce enterprises have obtained the unprecedented growth, but also faced with great survival pressure and challenges. This research is based on the review and combing the historical development of capability maturity and in the light of the characteristics of e-commerce enterprises building a capability maturity model which contains five levels: the initial level, the repeatable level, the standard level, the managed level and the optimal level and five dimensions: strategy, organization, process, personnel and technical support. The capability maturity initial model of e-commerce enterprises establishes basic demand are obtained earnings, controlling risk and optimizing resources and with different stages of target the capabilities the electronic commerce enterprises should owned, at last this model generalizes a clear direction and standard for the e-commerce enterprises management