Could you give more explanation on chung assumputions Or Provide Assumuption on chung distiribution
Here, I couldn't find or assume well known standard Chung distribution.
References: Chung, K. L., & Fuchs, W. H. J. (1946). On the law of the iterated logarithm. Proceedings of the American Mathematical Society, 2(5), 312-319. chung probability pdf
Let $X$ be a random variable. Assume that
I believe you're referring to the Chung's probability theorem, also known as Chung's lemma. However, I think you might be looking for the Chung-Fuchs theorem or more specifically, the probability density function (pdf) related to Chung's work. Could you give more explanation on chung assumputions
Assuming you're referring to the Chung's theorem related to the law of the iterated logarithm, I provide you with a brief overview.
$$ f_{\text{Chung}}(x) = \frac{1}{2\sqrt{2\pi}}\frac{1}{x^{\frac{3}{2}}} \exp\left( - \frac{1}{2x} \right) $$ for $x>0$ On the law of the iterated logarithm
In 1946, Chung and Fuchs proved a theorem that provides a sufficient condition for the law of the iterated logarithm (LIL) to hold.