Convergence of the θ-Euler-Maruyama method for a class of stochastic Volterra integro-differential equations
DOI:
https://doi.org/10.33993/jnaat532-1433Keywords:
Stochastic Volterra integro-differential equations, Θ-Euler-Maruyama method, strong convergence, H¨older continuity.Abstract
This paper addresses the convergence analysis of the θ-Euler-Maruyama method for a class of stochastic Volterra integro-differential equations (SVIDEs). At first, we discuss the existence, uniqueness, boundedness and H¨older continuity of the theoretical solution. Subsequently, the strong convergence order of the θ-Euler-Maruyama approach for SVIDEs is shown. Finally, we provided numerical examples to illustrate the theoretical results.
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