Amorphous silicon nitride is a key dielectric in silicon devices. The advantage of SiNx and Si3N4 over other dielectrics is that silicon nitride is compatible with silicon technology and is widely used in it. It is necessary to understand, experimentally and theoretically, the mechanism of charge transport in a memristor based on silicon nitride in the initial, high-resistance, and low-resistance states to develop a resistive memory element. At present, there is currently no single universal model of charge transport in a memristor based on silicon nitride. In our work, the charge transport of the initial, high, and low resistive states in an SiNx-based memristor is analyzed with four bulk-limited charge transport models. It is established that the Frenkel model of Coulomb traps ionization, Hill-Adachi model of overlapping Coulomb traps, and Makram-Ebeid and Lannoo model of multiphonon isolated traps ionization, quantitatively, do not describe the charge transport of the SiNx-based memristor in any state. The Nasyrov-Gritsenko model of phonon-assisted tunneling between traps gives a consistent explanation of the charge transport of the SiNx-based memristor in all states at temperatures above room temperature.