Abstract
We extend the new approach introduced in [24] and [25] for dealing with stochastic Volterra equations using the ideas of Rough Path theory and prove global existence and uniqueness results. The main idea of this approach is simple: Instead of the iterated integrals of a path comprising the data necessary to solve any equation driven by that path, now iterated integral convolutions with the Volterra kernel comprise said data. This leads to the corresponding abstract objects called Volterra-type Rough Paths, as well as the notion of the convolution product, an extension of the natural tensor product used in Rough Path Theory.
Acknowledgments
The authors are very grateful to the referees for their careful reading of the manuscript. We are particularly indebted to the referee who asks clarifications on the definitions and the proofs concerning the convolution product. This leads to substantial improvements in the clarity of the exposition.
Citation
Yvain Bruned. Foivos Katsetsiadis. "Ramification of Volterra-type rough paths." Electron. J. Probab. 28 1 - 25, 2023. https://doi.org/10.1214/22-EJP890
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