This article is cited in 10 papers

Short Communications

On the rate of convergence for the multidimensiona invariance principle

V. V. Gorodestkii

Leningrad

Abstract: In this paper, estimates of [1], [2] are generalized under some additional restrictions for the convergence to
1) a multidimensional Wiener process,
2) a Brownian sheet, i.e. a Gaussian random field $w(t)$, $t\in[0,1]$, $q>1$:
$$ \mathbf Ew(t)=0,\quad\mathbf Ew(t)w(s)=\prod_1^q(t_i\wedge s_i). $$


Received: 19.01.1974

 English version: Theory of Probability and its Applications, 1976, 20:3, 631–638

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