## The Annals of Probability

### Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes

Pranab Kumar Sen

#### Abstract

For a stationary $\phi$-mixing sequence of stochastic $p(\geqq 1)$-vectors, weak convergence of the empirical process (in the $J_1$-topology on $D^p\lbrack 0, 1 \rbrack)$ to an appropriate Gaussian process is established under a simple condition on the mixing constants $\{\phi_n\}$. Weak convergence for random number of stochastic vectors is also studied. Tail probability inequalities for Kolmogorov Smirnov statistics are provided.

#### Article information

Source
Ann. Probab., Volume 2, Number 1 (1974), 147-154.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996760

Digital Object Identifier
doi:10.1214/aop/1176996760

Mathematical Reviews number (MathSciNet)
MR402845

Zentralblatt MATH identifier
0276.60030

JSTOR
Sen, Pranab Kumar. Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes. Ann. Probab. 2 (1974), no. 1, 147--154. doi:10.1214/aop/1176996760. https://projecteuclid.org/euclid.aop/1176996760