Title: Multidimensional random motions with a natural number of finite velocities Show Chinese title

Title: 具有有限速度的自然数维度随机运动

Abstract: We present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some wide assumptions, we show the joint distribution of the position of the motion (both for the inner part and the border of the support) and the number of displacements performed with each velocity. Explicit results for cyclic and complete motions are derived. We establish useful relationships between motions moving in different spaces and we derive the form of the distribution of the movements in arbitrary dimension. Finally, we investigate further properties for stochastic motions governed by non-homogeneous Poisson processes. Show Chinese abstract

Abstract: 我们对在高维空间中以自然数个速度移动的随机运动进行了详细分析。 在所谓的最小随机动力学情况下，根据一些广泛假设，我们展示了运动的位置（包括内部部分和支撑集的边界）以及每个速度执行的位移次数的联合分布。 得到了循环运动和完整运动的明确结果。 我们建立了在不同空间中移动的运动之间的有用关系，并推导了任意维度中运动分布的形式。 最后，我们研究了由非齐次泊松过程支配的随机运动的进一步性质。