Transient nearest neighbor random walk and Bessel process

Details Transient nearest neighbor random walk and Bessel process Transient nearest neighbor random walk and Bessel process

2008-02-06

arxiv.org/abs/0802.0778v1

Mathematics

Probability

Scientific paper

We prove strong invariance principle between a transient Bessel process and a certain nearest neighbor (NN) random walk that is constructed from the former by using stopping times. It is also shown that their local times are close enough to share the same strong limit theorems. It is shown furthermore, that if the difference between the distributions of two NN random walks are small, then the walks themselves can be constructed so that they are close enough. Finally, some consequences concerning strong limit theorems are discussed.

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