On the anscombe condition for stochastic processes in a separable banach space

摘要

This paper treats the validity of A NSCOMBE-type conditions for special stochastic processes in a BANACH space. Such conditions concern the uniform continuity of sequences of stochastic processes and are useful for proving limit theorems of randomly indexed sums. The first part is devotes to stochastic processes with independent increments. The second part investigates stochastic processes generated by operator normed sums of weakly dependent random variables (strongly mixing or unigorm;y strongly mixing). The special case of operator normed sums of independent random varables in an EUCLIDEAN space was treated in GLESER 4, but these results are incorrect.