Abstract
The classical example of a large deviation result is Cramer’s theorem. It tells us, in a contemporary formulation, that if Y1, Y2,… is a sequence of independent real valued random variables with identical distribution function F such that
is finite for all finite θ,and if Zn = (Y1) + Y2 + … Yn/n then
satisfies
-
(0.1)
\( \overline {_{n \to \infty }^{\lim } } \frac{1} {\text{n}}\,\log \,\text{P}[z_n \, \in \text{A}]\, \leqslant \text{ } - \inf \text{ }k(a):a \in \text{A} \) A closed
and
-
(0.2)
\(\overline {_{n \to \infty }^{\lim } } \frac{1}{\text{n}}\,\log \,\text{P}[z_n \, \in \text{A}]\, \geqslant \text{ } - \inf \{ k(a):a \in \text{A}\}\) A Open.
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Orey, S. (1986). Large Deviations in Ergodic Theory. In: Çinlar, E., Chung, K.L., Getoor, R.K. (eds) Seminar on Stochastic Processes, 1984. Progress in Probability and Statistics, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6745-1_12
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