On the limit theorems for random variables with values in the spaces L p (2?pAcademic Article 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 fr Wahrscheinlichkeitstheorie und Verwandte Gebiete

author list (cited authors)

  • Pisier, G., & Zinn, J.

citation count

  • 48

complete list of authors

  • Pisier, Gilles||Zinn, Joel

publication date

  • January 1978