A Spectral Configuration Method For Stochastic Differential Equations Driven By Alpha-stable Processes

This thesis mainly uses the spectral collocation method to solve the stochastic differential equations driven by the o^-stable process.This method transforms the original problem into a matrix problem,which is significantly better then the finite difference method in calculation.Further,we apply the method to a class of stochastic differential equations with time-delay terms.The main contents and conclusions of this paper are as follows:Firstly,we propose a class of spectral collocation methods to numerically approximate stochastic differential equations driven by the o^-stable process.In this type of stochastic differ-ential equations,the drift term and diffusion term satisfy the global Lipschitz.We demonstrate the strong convergence of the numerical method.Subsequently,by employing different config-uration nodes,simulations are performed to prove that the proposed method outperforms the classical method.Secondly,we study the collocation method for stochastic delay differential equations driven by the 〇;-stable process.We give a specific format and also further prove the feasibility of the method when studying the spectral collocation method for the time-delay problems.Finally,a series of parameter settings are used to verify the feasibility of the method for specific equations.