Summary: On the law of the iterated logarithm for
Gaussian processes 1
Miguel A. Arcones 2
Suggested running head: L.I.L. for Gaussian processes
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We present some optimal conditions for the compact law of the iterated logarithm of a
sequence of jointly Gaussian processes in different situations. We also discuss the local law of
the iterated logarithm for Gaussian processes indexed by arbitrary index sets, in particular
for self­similar Gaussian processes. We apply these results to obtain the law of the iterated
logarithm for compositions of Gaussian processes.
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Key words: Gaussian processes, law of the iterated logarithm, self­similar processes.
1
Research partially supported by NSF Grant DMS­93­02583.
AMS 1991 subject classifications. Primary 60F15, 60G15.
2
Department of Mathematics, University of Utah, Salt Lake City, UT 84112. arcones@math.utah.edu.
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1. INTRODUCTION.
We consider different kinds of laws of the iterated logarithm (L.I.L.) for Gaussian pro-

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

Collections: Mathematics