马尔可夫随机过程中移动对象的空间特征分析及近似逼近研究

研究一类移动对象在马尔可夫（马氏）随机过程中的空间逼近问题.首先运用数学推理方式获得时空网络马尔可夫随机模型的一种状态转移函数.定义时空网络为移动对象及其移动轨迹形成的三维空间，建立马尔可夫随机过程的距离空间，证明了相应环境下的不动点理论.通过分析和扩展状态转移函数得到距离空间的自映射算子，从原节点映射到目标节点，达到对象的移动，并对此进行了理论证明和仿真实验验证.在此基础上从应用层面出发，尝试性地进行了移动对象的空间粒度分解，利用不动点映射更好地定位移动对象，实时满足移动对象的需求.相关实验进一步验证了空间分析的可行性和有效性. 关键词： 马尔可夫随机过程 距离空间 不动点 自映射算子

Moving object in Markov stochastic processes: spacial characteristic analysis and approximate approach research

In this paper, space approach of moving object in a kind of Markov stochastic process is studied. A state transfer function of Markov stochastic model in space-time network is deduced by mathematic method firstly. The space-time network is defined as a three-dimensional space which is formed from moving objects and their trajectories, and the corresponding distance space is constructed. Then the fixed point theorem is presented. A self-mapping operator in the distance space is attained by the analysis of state transfer function. On the basis of the above theory, the moving object can be mapped from the former node to the target one by themselves. All of these are proved by theorems and emulational experiments. Moreover, we attempt to use the method of space decompounds with granularity in moving object. The moving object can be approached better through the mapping of fixed point, and the requirements of moving objects are satisfied in real time. The relevanr experiments also validate the feasibility and validity of space approach idea.