LIMIT-THEOREMS FOR RANDOM-VARIABLES WITH VALUES IN SPACES LP (2LESS-THAN-OR-EQUAL-TO P LESS-THAN INFINITY) uri icon

abstract

  • We prove that whenever B is an infinite dimensional Banach space, there exists a B-valued random variable X failing the Central Limit Theorem (in short the CLT) and such that IEX 2 = but yet satisfying the Law of the Iterated Logarithm (in short the LIL). We obtain a new sufficient condition for the LIL in Hilbert space and we characterize the random variables with values in l p or L p with 2

published proceedings

  • ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE

author list (cited authors)

  • PISIER, G., & ZINN, J.

citation count

  • 56

complete list of authors

  • PISIER, G||ZINN, J

publication date

  • December 1978