**Abstract:**
We prove large deviation principles (LDP) for *m*-fold products of empirical
measures and for *U*-empirical measures, where the underlying sequence of
random variables is a special Markov chain, an exchangeable sequence, a mixing
sequence or an independent, but not identically distributed, sequence. The LDP can
be formulated on a subset of all probability measures, endowed with a topology which
is even finer than the usual tau-topology. The advantage of this topology is that
taking the integral of *f* is a continuous operation even for certain
unbounded *f* taking values in a Banach space. As a particular application we
get large deviation results for *U*-statistics and *V*-statistics based
on dependent sequences. Furthermore, we prove an LDP for products of empirical
processes in a topology, which is finer than the projective limit tau-topology.

**Keywords:**
large deviations,
exponential approximations,
contraction principle,
weak topology,
tau topology,
Markov chains,
exchangeable sequences,
mixing sequences,
*U*-empirical measures,
*U*-statistics,
*V*-statistics

**Reference:**
Markov
Processes and Related Fields, Vol. 7, No. 3 (2001) 435-468.

**2010
Mathematics Subject Classification:**

- 60F10 Large deviations

The paper (26 pages, revised version May 12, 2001) is available in:

- PDF / portable document format (315 kB)

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