两参数齐次独立增量过程在原点的局部性质

Some Properties of Two parameter Stochastic Processes with Stationary Independent Increments in an Origin

中文关键词:  独立增量过程  累积量  局部增长．

英文关键词:stochastic processes with stationary independent increments  accumulation  local growth.

中文摘要:

      Ａｄｌｅｒ曾经给出了两参数独立增量过程的特征函数的一般形式．本文对齐次情形给出了更具体的表达式，引进了累积量的概念．在此基础上，研究了比值Ｘ（ｓ，ｔ）／ｓｔ在原点的分布，单调过程在原点的局部性质以及任意过程在原点的局部增长．由此得到了Ｂｒｏｗｎ单和不包含高斯分量的过程在原点的局部增长．

英文摘要:

      The general form of characteristic function of two parameter stochastic processes with independent increments has been given in [2]. As for stationary case, we give a more general form of characteristic function, and discuss the distribution of ratio X(s,t)/st , local properties of the monotonous processes and local growth of any processes in an origin. From this, we obtain the local growth properties of Brownian sheet and the processes without Gauss moment.