Some problems related to the functional law of the iterated logarithm

by    Natalia Gorn

Preprint series: 99-33 , Reports on Analysis

Abstract: Abstract:

The law of the iterated logarithm is one of the most important
limit theorems in the probability theory. In the dissertation
is the functional form of this law considered. We present a review
of the basic known results (Chapter 1) and also the following our new
results.
In Chapter 2 we consider the space of all continiuos functions endowed
with some lower semi-continuous norm and prove a simple necessary
and sufficient condition which should be imposed on this norm so that
the functional law of the iterated logarithm for the increments of
the Wiener process (generalized functional Revesz law) is valid
in the corresponding Banach space.
In Chapter 3 the cluster sets for partially observed processes are
studied. We describe the cluster set for partial sum process generated
by independent non-identically distributed random values satisfiyng some
condition of Lindeberg type (the Egorov condition). This condition is
also proved to be quite optimal.
In Chapter 4 we solve the problem of the exact convergence rate in
Chung's functional law for the so-called 'slowest points'. Our description
is closely related to the study of an interesting functional emerging from
the large deviation problem for the Wiener process in a strip.



Keywords: functional law of the iterated logarithm, Wiener process, Revesz law, Chung's law

Notes: Dissertation 15.04.99 (W. Linde)

Upload: 1999-06-09


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