Abstract:
A unified theory is constructed which describes the
a.s. (almost
surely) behavior of increments of stochastically continuous
homogeneous processes with independent increments. This theory
includes the strong law of large numbers, the Erdös–Rényi
law, the Shepp law, the Csörgő–Révész law, and
the law of the iterated logarithm. The range of applicability of the
results is extended from several particular cases to the whole
class of stochastically continuous homogeneous processes with
independent increments.
Keywords:increments of processes with independent increments, Erdös–Rényi law, Shepp law, the law of large numbers, the law of the iterated logarithm.
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