國立清華大學 數學系

Abstract: For a sequence of correlated square integrable random variables $\{X_n, n\geq 1\}$, conditions are provided for the strong law of large numbers $\lim_{n\rightarrow \infty} \frac{ S_{n}- ES_{n} }{ n }=0$ almost surely to hold where $\ S_{n}=\sum^n_{i=1}{X_{i},n \geq 1}$. The hypotheses stipulate that two series converge, the terms of which involve, respectively, both the Golden Ratio $\varphi=\frac{1 + \sqrt{5}}{2}$ and bounds on Var$X_n$ (respectively, bounds on Cov$(X_n, X_{n+m}))$. An application to first passage times is provided. Tea Time: 3:30PM, R707