Model order reduction for stochastic differential equations driven by standard and fractional Brownian motion

Abstract

This dissertation investigates model order reduction (MOR) for high-dimensional stochastic differential equations (SDEs) and spatially discretized stochastic partial differential equations (SPDEs) driven by standard and fractional Brownian motion. Efficient MOR schemes are developed for unstable stochastic systems using Gramian-based approaches and Lyapunov equations, complemented by variance-reduced sampling methods. Error bounds are derived to guide reduced system dimension. For systems driven by fractional Brownian motion with H ∈ [1/2,1), empirical reduction techniques using Young and Stratonovich interpretations are proposed. Numerical experiments confirm the computational efficiency and accuracy of the presented MOR strategies in stochastic settings.