The main objective of this article is to solve stochastic delay differential equations via Haar wavelets. We present fundamental concepts of stochastic process, Haar, block pulse functions, and their operational matrix relevant to time-delayed Haar. Analytic solutions of two examples are solved for the first time to approximate two kinds of single time-delayed stochastic differential equations with additive and multiplicative noise. This orthogonal basis function not only simplifies the problem but also speeds up the computations and lessens the computational complexity of the stochastic delay differential equations to a lower triangular system of linear algebraic equations. The equation can be solved via forward substitution, such as lower-upper decomposition method. Finally, we examine the order of convergence and error analysis of two visual samples to validate the efficiency and effectiveness of the suggested procedure.
Kiaee, S. N., Khodabin, M., & Ezzati, R. (2024). Approximation of stochastic delay differential equations based on Haar functions. Journal of Statistical Modelling: Theory and Applications, 5(1), 33-52. doi: 10.22034/jsmta.2024.21318.1132
MLA
Seyedeh Neda Kiaee; Morteza Khodabin; Reza Ezzati. "Approximation of stochastic delay differential equations based on Haar functions", Journal of Statistical Modelling: Theory and Applications, 5, 1, 2024, 33-52. doi: 10.22034/jsmta.2024.21318.1132
HARVARD
Kiaee, S. N., Khodabin, M., Ezzati, R. (2024). 'Approximation of stochastic delay differential equations based on Haar functions', Journal of Statistical Modelling: Theory and Applications, 5(1), pp. 33-52. doi: 10.22034/jsmta.2024.21318.1132
VANCOUVER
Kiaee, S. N., Khodabin, M., Ezzati, R. Approximation of stochastic delay differential equations based on Haar functions. Journal of Statistical Modelling: Theory and Applications, 2024; 5(1): 33-52. doi: 10.22034/jsmta.2024.21318.1132
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