The recent co-optimization of memristive technologies and programming algorithms enabled neural networks training with in-memory computing systems. In this context, novel analog filamentary conductive-metal-oxide (CMO)/HfO_x redox-based resistive switching memory (ReRAM) represents a key technology. Despite device performance enhancements reported in literature, the underlying mechanism behind resistive switching is not fully understood. This work presents the first physics-based analytical model of the current transport and of the resistive switching in these devices. As a case study, analog TaO_x/HfO_x ReRAM devices are considered. The current transport is explained by a trap-to-trap tunneling process, and the resistive switching by a modulation of the defect density within the sub-band of the TaO_x that behaves as electric field and temperature confinement layer. The local temperature and electric field distributions are derived from the solution of the electric and heat transport equations in a 3D finite element ReRAM model. The intermediate resistive states are described as a gradual modulation of the TaO_x defect density, which results in a variation of its electrical conductivity. The drift-dynamics of ions during the resistive switching is analytically described, allowing the estimation of defect migration energies in the TaO_x layer. Moreover, the role of the electro-thermal properties of the CMO layer is unveiled. The proposed analytical model accurately describes the experimental switching characteristic of analog TaO_x/HfO_x ReRAM devices, increasing the physical understanding and providing the equations necessary for circuit simulations incorporating this technology.