Rough path lifts of Banach space-valued Gaussian processes

A.A. Kalinichenko

Stochastic Processes and their Applications, 2025, vol. 190, issue C

Abstract: Under certain assumptions on a Gaussian process taking values in a separable Banach space, we construct its lift to a geometric rough path. The lift is natural in the sense that for any sequence of piece-wise linear approximations to the original process, their signatures converge to the lifted path in a suitable metric. This extends to infinite dimensions the known results in Euclidean spaces. Examples of processes satisfying our conditions include the infinite-dimensional analogues of Brownian motion, fractional Brownian motion with Hurst parameter H∈(14,12], Ornstein–Uhlenbeck process. As a by-product of our methods, we also provide a construction for Ito–Skorokhod integrals of these processes, which might be of independent interest.

Keywords: Rough paths; Rough differential equations; Infinite-dimensional stochastic analysis; Gaussian processes (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104739

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