Innovation capability of enterprises will greatly influence the current and future development of companies. This paper investigates the relationship between customer concentration and innovation capability of enterprises through the view of both the financing constraints and the expectation of managers. Based on the data of China’s A-share listed companies over the period from 2012 to 2016, several methods including system GMM, threshold model of fixed effects, and PSM are applied for empirical analysis. The results show that the innovation capability of listed companies in China are negatively correlated with the customer concentration. Higher customer concentration brings about stronger constraints from large customers on enterprises and greater dependence of enterprises on large customers, which result in weaker demand for innovation and lower investment in innovation. Meanwhile, the results demonstrate the double-threshold effect of financing constraints. The effect of customer concentration on innovation can be different in companies with low, medium, or high-financing constraints. Furthermore, optimistic expectations are more conducive to the reduction of customer concentration and the improvement of innovation. In addition, based on the perspective of the manager’s expectation, the research demonstrates the heterogeneous impact of manager’s expectation on the relationship between customer concentration and innovation capability.

In this paper, we establish a large deviation principle for a mean reflected stochastic differential equation driven by both Brownian motion and Poisson random measure. The weak convergence method plays an important role.

In this paper, we establish a central limit theorem and a moderate deviation principle for the positive diffusions, including the CEV and CIR models. The proof is based on the exponential approximations theorem and Burkholder-Davis-Gundy’s inequality.

In this paper, we study the central limit theorem for a perturbed stochastic heat equation in the whole space $\mathbb{R}^{d}$Rd , $d\ge 1$d≥1 . This equation is driven by a Gaussian noise, which is white in time and correlated in space, and the differential operator is a fractional derivative operator. Burkholder’s inequality plays an important role in the proof.