1. A moving object prediction device comprising: a moving object detection section that detects a position, and a behavior state or a movement state, of a moving object in a detection target range; a region detection section that detects a plurality of categories of regions of track segment and regions of stationary object in the detection target range; a map generation section that generates 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 section; a moving object recording section that generates a position distribution 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 section, and records the distributions on the presence probability map; and a prediction section that moves the moving object position distribution based on the moving object movement state distribution, changes the moved position distribution based on presence probabilities of the presence probability map, and predicts a future position distribution of the moving object on the presence probability map.