We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a convergent series expansion of the autocorrelation function in powers of the ratio between mean and standard deviation of the underlying Gaussian process. We apply the results to two sample processes, and we validate the theoretical results with simulations based on standard signal processing techniques.

翻译：本文研究了通过非零均值高斯过程的乘法逆运算得到的随机过程的谱特性。我们证明了对于大多数正则过程，其自相关函数与功率谱均存在，并找到了自相关函数关于原高斯过程均值与标准差比值的幂级数展开式，该级数具有收敛性。我们将研究结果应用于两个示例过程，并基于标准信号处理技术通过仿真验证了理论结果。