Asymptotic representations in Stochastic Process Approximations

作者：Zhang, Zhihua^*

来源：Journal of Computational Analysis and Applications, 2015, 18(4): 672-684.

• stochastic process
• decomposition
• Fourier cosine coefficient
• asymptotic representation

Fourier cosine transforms are applied widely in applied mathematics, PDEs, and signal processing. In this paper we give some asymptotic representations in stochastic Fourier cosine analyses based on our decomposition. More importantly, we propose a stochastic Fourier cosine expansion with a polynomial term. In this expansion, Fourier cosine coefficients decay fast such that we can reconstruct stochastic processes by using the least coefficients. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions.

• 出版日期2015-4
• 单位北京师范大学