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On the character of convergence to Brownian local time. II. (English) Zbl 0572.60079
[For part I see the foregoing review, Zbl 0572.60078.]
In this paper we consider the sequences of stochastic processes which converge weakly as \(n\to \infty\) to Brownian local time. These processes are generated by a recurrent random walk with finite variance. The main result is the following:
It is possible to redefine a random walk in such a way that for a wide class of processes the normalized differences between them and Brownian local time converge in distribution to some stochastic process. We also prove that such differences with probability one have the logarithmic upper bound. It is the so called ”strong invariance principles for local times”.

60J65 Brownian motion
60J55 Local time and additive functionals
Full Text: DOI
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