When watching a video, the viewer's eyes will fixate on a certain point within each frame. Areas far from the viewers gaze location are perceived with much lower visual acuity than those around the fixation point. This effect is known as foveation. In this paper, the effect of foveation on High Dynamic Range (HDR) video perception is investigated. Using eye tracking data recorded from six different HDR sequences, the bit depth of individual frames are variably encoded, with the pixels with the highest bit depth corresponding to areas around the most likely fixation point for the frame. The bit depth of pixels within the modified frame will then gradually reduce, dependent on how far the pixel is located from the fixation point. To lower the bit depth of the HDR content, a tone mapping operator (TMO) is used. The particular TMO that is used generates an optimal tone mapping curve for every frame, which is used for both tone mapping to reduce the bit depth, and for inverse tone mapping for display purposes. However, this procedure can often cause large amounts of flickering, as well as banding artefacts, which reduce the perceptual quality of the video. Methods to mitigate these effects are proposed and implemented in this paper. Subjective performance evaluations were carried out involving 17 participants in order to evaluate the proposed methodology. Results show that when the lowest bit depth is 8 bits, the modified video is indistinguishable from the original. However, when 6 bit regions are introduced, a significant difference is noticed. Dithering and increasing the foveation region significantly improves the perceptual quality of the modified sequence.