Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 4, 670--673

On Weak Convergence in ${\mathcal{M}}\left(H\right)$

Suman Majumdar, University of Connecticut, Stamford, USA

SUMMARY. A sequence $\left\{X_n\right\}$ of random elements taking values in a real separable Hilbert space $H$ converges in distribution to a $H$-valued random element $X$ if the sequence of linear functionals $\left\{<X_n,x>\right\}$ converges in distribution to $<X,x>$ for every $x\in H$ and $\left\{\|X_n\|\right\}$ converges in distribution to $\|X\|$.

AMS (2000) subject classification. Primary 60B10.

Key words and phrases. Convergence in distribution, convergence in probability, Skorohod-Dudley-Wichura representation.

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