n—指标诸可测性和基本过程类

VARIOUS MEASURABILIES AND BASIC CLASSES Of STOCHASTIC PROCESSES INDEXD BY T=[0, 1]~n

本文建立n—指标随机过程一般理论所必须的基本概念,各种循序可测性,可选可测性和可料可测性,N—指标鞅论所涉及的基本过程类。两指标鞅论最近出了一本系统性总结的专著,其作者认为那些结果很有希望推广到任意有限维指标的情形。本文可视为这种推广的最初实现,虽然只涉及概念和那些容易的部分,但也是不可少的部分,其它需要克服更多困难的专题将另文加以讨论。

In this paper, we establish the basic concepts neededfes for the genoral theory of n parameter stochastic processes including various progiessive mesurabilities, optoinal measurabbilities and prodictable measurabilities, discuss basic classes of stochastic processes concerning n parametes martingale theory the other aspects about the general theory of n parameter stochadtic processes based on the concepts introduced here.