2011Theory of Probability and Mathematical StatisticsOpen access

Law of the iterated logarithm for solutions of stochastic equations

D. S. Budkov, S. Ya. Makhno

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Abstract

Strassen’s law of the iterated logarithm for a solution $x(t)$ of Itô’s stochastic equation is considered in the paper. We obtain a result for small times in the uniform metric and for a more general normalizing function than the classical $\sqrt { h\ln \ln \frac {1}{h}}$.

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Strassen’s law of the iterated logarithm for a solution $x(t)$ of Itô’s stochastic equation is considered in the paper. We obtain a result for small times in the uniform metric and for a more general normalizing function than the classical $\sqrt { h\ln \ln \frac {1}{h}}$.

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Available abstract

Strassen’s law of the iterated logarithm for a solution $x(t)$ of Itô’s stochastic equation is considered in the paper. We obtain a result for small times in the uniform metric and for a more general normalizing function than the classical $\sqrt { h\ln \ln \frac {1}{h}}$.

Key concepts: Law of the iterated logarithm, Mathematics, Iterated logarithm, Logarithm, Applied mathematics, Natural logarithm, Iterated function, Mathematical analysis

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