Let $X$ be a random variable. Assume that
If you provide more information or clarify which Chung probability distribution or theorem (e.g., Chung-Fuchs, Chung-Lai, or Chung-Sobel) you are referring to, I may provide you a more accurate response and high-quality equations. chung probability pdf
In 1946, Chung and Fuchs proved a theorem that provides a sufficient condition for the law of the iterated logarithm (LIL) to hold. Let $X$ be a random variable
$$ f_{\text{Chung}}(x) = \frac{1}{2\sqrt{2\pi}}\frac{1}{x^{\frac{3}{2}}} \exp\left( - \frac{1}{2x} \right) $$ for $x>0$ or Chung-Sobel) you are referring to