A convergent wavelet-based method for solving linear stochastic differential equations included 1D and 2D noise
Nasim Madah Shariati, Mohammad Reza Yaghouti, Amjad Alipanah · Journal of Statistical Computation and Simulation · 2022
In this paper, we present a Collocation method based on scaling function of Daubechies Wavelet(CDW) to solve linear stochastic differential equations with one and two dimensional noise. By applying this method, the problem transforms to a linear system of algebraic equations with coefficients of expansion as unknowns. Due to interesting properties of the Daubechies wavelet such as orthogonality, compactly support and vanishing moments, the coefficients of expansion are obtained fast. The convergence of the proposed method is presented. To verify the accuracy and efficiency of the proposed method some numerical examples are provided.