Path independence for the additive functionals of stochastic Volterra equations with singular kernels and Hölder continuous coefficients

In this paper, we are concerned with stochastic Volterra equations with singular kernels and H & ouml;lder continuous coefficients. We first establish the well-posedness of these equations by utilizing the YamadaWatanabe approach. Then, we aim to characterize the path-independence for additive functionals of these equations. The main challenge here is that the solutions of stochastic Volterra equations are not semimartingales nor Markov processes, thus the existing techniques for obtaining the path-independence of usual, semimartingale type stochastic differential equations are no longer applicable. To overcome this difficulty, we link the concerned stochastic Volterra equations to mild formulation of certain parabolic type stochastic partial differential equations, and further apply our previous results on the path-independence for stochastic evolution equations to get the desired result. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.