Wong-Zakai Approximations for Stochastic Volterra Equations (Journal of Computational Mathematics, 2024)
In this paper, we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions. We may apply it to a class of stochastic differentialequations with the kernel of fractional Brownian motion with Hurst parameter $H ∈ (1/2, 1)$ and subfractional Brownian motion with Hurst parameter $H ∈ (1/2, 1).$ As far as we know,this is the first result on stochastic Volterra equations in this topic.
Keywords: Stochastic Volterra equations; Wong-Zakai approximations; Fractional Brownian motion; Subfractional Brownian motion; Quadratic mean convergence.