Well‐Posedness and Regularity of Solutions for Stochastic Volterra Integral Equations With General Weakly Singular Kernels

ABSTRACT We explore the well‐posedness and regularity of solutions for stochastic Volterra integral equations with general weakly singular kernels (SVIEGK). The kernels considered satisfy and . By employing a suitably weighted norm and Lebesgue's dominated convergence theorem, we establish the well‐posedness of solutions, including their existence, uniqueness, and continuous dependence on the initial value as well as on the parameters and . Additionally, for kernels with a specific structure, we extend the Hölder regularity results for stochastic Volterra integral equations.