Abstract: Probabilistic time geography (PTG) is suggested as an extension of (classical) time geography, in order to present the uncertainty of an agent located at the accessible position by probability. This may provide a quantitative basis for most likely finding an agent at a location. In recent years, PTG based on normal distribution or Brown bridge has been proposed, its variance, however, is irrelevant with the agent's speed or divergent with the increase of the speed; so they are difficult to take into account application pertinence and stability. In this paper, a new method is proposed to model PTG based on Markov chain. Firstly, a bidirectional conditions Markov chain is modeled, the limit of which, when the moving speed is large enough, can be regarded as the Brown bridge, thus has the characteristics of digital stability. Then, the directed movement is mapped to Markov chains. The essential part is to build step length, the state space and transfer matrix of Markov chain according to the space and time position of directional movement, movement speed information, to make sure the Markov chain related to the movement speed. Finally, calculating continuously the probability distribution of the directed movement at any time by the Markov chains, it can be get the possibility of an agent located at the accessible position. Experimental results show that, the variance based on Markov chains not only is related to speed, but also is tending towards stability with increasing the agent's maximum speed.

Key words: probabilistic time geography, Markov chains, directed movements, prism