Randomisation of rough stochastic differential equations

Peter K. Friz; Khoa Le; Huilin Zhang

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arXiv · 2503.06622

Randomisation of rough stochastic differential equations

Peter K. Friz·Khoa Le·Huilin Zhang

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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.

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Peter K. Friz, Khoa Le, Huilin Zhang. 2025-03-09. Randomisation of rough stochastic differential equations. https://arxiv.org/abs/2503.06622

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