Inhomogeneous affine Volterra processes

We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions equations driven by a Brownian motion with an kernel K(t,s) and drift diffusion coefficients b(s,Xs) σ(s,Xs). In case b σσT we show how conditional Fourier–Laplace functional can be represented solution Riccati–Volterra integral equation. For convolution type K(t,s)=K¯(t−s) establish existence stochastic If in addition are affine, prove that is exponential–affine past path. Finally, apply these extension rough Heston model used mathematical finance.