Averaging principle for slow-fast systems of PDEs with rough drivers

2025/10/25 by Li, Miaomiao, Pei, Bin, Xu, Yong +1
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.22269

Abstract

This paper investigates a class of slow--fast systems of rough partial differential equations defined over a monotone family of interpolation Hilbert spaces. By employing the controlled rough path framework tailored to a monotone family of interpolation spaces, together with a time discretization argument, we demonstrate that the slow component strongly converges to the solution of the averaged system in the supremum norm as the time-scale parameter ε tends to 0.

Citations

• Averaging principle for rough slow-fast systems of level 3
• Rough differential equations in the flow approach
• Moderate deviations for rough differential equations
• Almost Sure Averaging for Fast-slow Stochastic Differential Equations via Controlled Rough Path
• Almost Sure Averaging for Evolution Equations driven by fractional Brownian motions
• Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients
• Averaging principle for slow-fast systems of rough differential equations via controlled paths
• Precise Laplace approximation for mixed rough differential equation
• Strong Convergence Rates in Averaging Principle for Slow-Fast McKean-Vlasov SPDEs
• Global solutions for semilinear rough partial differential equations
• Global solutions for semilinear rough partial differential equations
• Slow-fast systems with fractional environment and dynamics
• Pathwise unique solutions and stochastic averaging for mixed stochastic partial differential equations driven by fractional Brownian motion and Brownian motion
• Averaging Principles for Mixed Fast-Slow Systems Driven by Fractional Brownian Motion
• Averaging principle for slow-fast stochastic partial differential equations with Hölder continuous coefficients
• Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma
• Strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients
• Global solutions and random dynamical systems for rough evolution equations
• Hörmander's theorem for semilinear SPDEs
• Local mild solutions for rough stochastic partial differential equations
• Rough differential equations with unbounded drift term
• Eikonal equations and pathwise solutions to fully non-linear SPDEs
• Non-linear Rough Heat Equations
• A Khasminskii type averaging principle for stochastic reaction-diffusion equations
• Averaging principle for a class of stochastic reaction-diffusion equations
• Partial differential equations driven by rough paths

Related

• Averaging principle for slow-fast systems of rough differential equations via controlled paths
• Averaging principle for semilinear slow-fast rough partial differential equations
• Averaging principle for rough slow-fast systems of level 3
• Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients
• Almost Sure Averaging for Fast-slow Stochastic Differential Equations via Controlled Rough Path