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In this paper, we propose an architecture of software-defined information-centric network virtualization with device-to-device (D2D) communications, which facilitates dynamic virtual resource allocation and content caching via a software-defined networking (SDN) controller with a global view of the system. In our proposed framework, substrate physical resources can be virtualized and shared among multiple mobile virtual network operators (MVNOs). Meanwhile, by means of integrating D2D communications into information-centric wireless networks, content caching is enabled not only in the air but in mobile devices as well. In addition, taking into consideration inaccurate channel estimation and measurement, we formulate the virtual resource allocation and caching optimization as a discrete stochastic optimization problem in which imperfect channel state information is incorporated. Because the formulated virtual resource allocation problem is a large-scale combinational optimization problem, we exploit discrete stochastic approximation approaches to cope with it. Finally, extensive simulations are conducted to demonstrate the effectiveness of the proposed scheme with different system parameters. Simulation results show that MVNOs can benefit from not only the sharing of physical infrastructure but from the caching functionality that exists in both the air and mobile devices as well. [ABSTRACT FROM PUBLISHER]