Randomisation of rough stochastic differential equations

Abstract

Rough stochastic differential equations (RSDEs) are common generalisations of Ito SDEs and Lyons RDEs and have emerged as new tool in several areas of applied probability, including non-linear stochastic filtering, pathwise stochastic optimal control, volatility modelling in finance and mean-fields analysis of common noise system. We here take a unified perspective on rough Ito processes and discuss in particular when and how they become, upon randomisation, "doubly stochastic" Ito processes, and what can be said about their conditional laws.