Variation of constants formulae for forward and backward stochastic Volterra integral equations

In this paper, we provide variation of constants formulae for linear (forward) stochastic Volterra integral equations (SVIEs, short) and Type-II backward (BSVIEs, in the usual Itô's framework. For these purposes, define suitable classes kernels introduce new notions products adapted L2-processes. Observing algebraic properties products, obtain by means corresponding resolvent. Our framework includes SVIEs with singular such as fractional differential equations. Also, our results can be applied to general BSVIEs infinitely many iterated integrals. The duality principle between generalized is also proved.