1. A moving object prediction device comprising: a processor including: a moving object detection module to detect a position, and a behavior state or a movement state, of a moving object in a detection target range; a region detection module to detect a plurality of track segment regions and stationary object regions in the detection target range; a map generation module configured to generate a presence probability map in which a presence probability expressing a presence likelihood or presence unlikelihood of a moving object is applied to the track segment regions and the stationary object regions detected by the region detection module; a moving object recording module configured to generate a position distribution represented by a plurality of moving object particles and a movement state distribution of the moving object based on the position and the behavior state or the movement state of the moving object detected by the moving object detection module, and record the distributions on the presence probability map; and a prediction module configured to move the position distribution based on the movement state distribution, change the moved position distribution based on presence probabilities of the presence probability map, and predict a future position distribution of the moving object on the presence probability map.