In this paper we present the result of successively applying a Chebyshev polynomial to a continuous random variable. In particular we show that under mild assumptions the limiting distribution will be the same as the weight with respect to which Chebyshev polynomials are orthogonal.

翻译：本文研究了连续随机变量经切比雪夫多项式连续变换后的极限分布特性。特别地，我们证明了在温和假设条件下，极限分布与切比雪夫多项式正交权函数相同。