Convergence Analysis Of The Truncated Euler Method For A Class Stochastic Delay Volterra Integro-differential Equations

Volterra integro-differential equations(VIDEs)are widely used in biology and medi-cine and many other fields.However,systems are not only affected by random factors,but also related to the historical state of the past.The study of stochastic delay Volterra integro-differential equations(SDVIDEs)is significant.In practice,the exact solution of the equation is difficult to get the expression.In addition,the particularity of Volterra integral term in the equation makes it more difficult to solve SDVIDEs.Therefore,it is of great significance to study SDVIDEs numerical methods for solving this problem.This thesis mainly studies the convergence of truncated Euler method for a class of SDVIDEs.First,we introduce the theoretical analysis and numerical analysis of equations relat-ed to SDVIDEs.Meanwhile,we give some important inequalities and properties needed to study the problems in this thesis.Next,we present the existence,uniqueness and pth moment boundedness of the exact solution of SDVIDEs under of local Lipschitz condition and Khasminskii type con-dition.Finally,we construct the truncated Euler method of SDVIDEs and prove its pth mo-ment boundedness.On this basis,we investigate its strong convergence in qth(q ?[2,p))moment.We also discuss its convergence rate when the drift term f and diffusion term g satisfy the polynomial growth condition and Khasminskii type condition,the conclusions are verified by numerical examples.