A continuous analogue of the invariance principle and its almost sure version

Details A continuous analogue of the invariance principle and its almost sure version A continuous analogue of the invariance principle and its almost sure version

2009-08-07

arxiv.org/abs/0908.1072v1

Publ. Math. Debrecen, 70/1-2 (2007), 203-210

Mathematics

Probability

6 pages

Scientific paper

We deal with random processes obtained from a homogeneous random process with independent increments by replacement of the time scale and by multiplication by a norming constant. We prove the convergence in distribution of these processes to Wiener process in Skorokhod space endowed by the topology of uniform convergence. An integral type almost sure version of this theorem is obtained.

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