具有平稳增量的自相似过程的边缘分布

On Marginal Distribution of Self-similar Processes with Stationary Increments

设{}0),(=tXXt是指数)0(>H型的具有平稳增量的自相似过程,论文给出了1X的边缘分布的一些结果. 对于1H,1logX+的压缩函数有一个只依赖于H的界;对0>H,1X除了一些平凡的情形外是非原子的;而对1>H,1X的尾分布的下界也给出了;文章的最后对1X的支撑的连通性给予了讨论,并给出了一些结果.

Let {}0 ),(=tXXt be a real-Valued stochastic process which is self-similar with parameter 0>H and has stationary increments. Sevaral results about the marginal distribution of 1X are given. For 1H, there is a bound depending only on H, on the concentration function of +1logX. For all 0>H, 1X cannot have any atoms except in certain trivial cases. Some lower bounds are given for the tails of the distribution of 1X in case 1>H, Finally, some results are given concerning the connectedness of the support of 1X.