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This papers develops a stochastic integration theory with respect tovolatility modulated L\'{e}vy-driven Volterra (VMLV) processes. It extendsrecent results in the literature to allow for stochastic volatility and purejump processes in the integrator. The new integration operator is based onMalliavin calculus and describes an anticipative integral. Fundamentalproperties of the integral are derived and important applications are given.

On stochastic integration for volatility modulated L\'{e}vy-driven Volterra processes